A masterfully systematic breakdown of algebraic fundamentals that provides students with a clear, logical roadmap for solving complex equations. It is a quintessential example of pedagogical clarity in foundational mathematics.
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10th class math 1b question answer | class 10 math 1b | pratikalpana apasarana bajragunanaAdded:
So hello everyone welcome to classroom Exercise one.
Okay.
Question number one. Question number one question number x + y - 8 = 2x - 3 yus = 0 Okay.
Okay.
X + Y + 8 X - Okay.
2x - 3 into y.
8 - x -1 = 2xus - - + 3 into x 3x -1 = 0 Okay, next 3x + 2x 5 x next -4 - 1 - 25= 5 minus value.
Next.
Okay.
Okay.
Question number one.
number 3x + 2 y - 5 = x - 3 y - 9 = 0 3x + 2 y - 5 = 0 to 2x 5 - 3x 5 - 3x 2. The next x - 3 y - 9 - 9 x - 3 into y 5 - 3x 5 - 3x by 2 next - 9= 0. Next - 9 = 0. Next.
Okay.
9x + 2x 11us 113 x 33 by 11 x Next.
Next.
Okay.
Y = 5 - 3x 2. y = 5 - 3x 2. 5 - 3 into x.
No.
Okay. Yus 2 answer number three 2x - 5 y + 8 = x - 4 y + 7 = 0. Okay.
2x - 5 y + 8 = 0= - 5 y + 5 y 8 x= 5 y - 8.
Okay.
x - x - 4 y + 7 = 0 x 5 y - 8 5 y - 8 by 2 - 4 y + 7 = 0 next 5 Y next 5 y - 8 y - 3 y next.
Okay. - 3 y = y= next. Next.
X = 5 Y 5 into - 8 by 2. Next answer question number.
Next number 11 x + 15 y + 23 = 0. Say 7 x - 2 y - 20 = 0.
First 11 x + 15 y + 23 = 0 15 y = 23 - 23 11 x - 11 x - 11 - 23 - 11 x - 23 Okay.
Next.
Next. 7 x - 2 y - 20 = 0.
7 x - 2 into y. - 2 into y. Okay. - 11 x - 23 by 15. Okay. Next - 20 = 0. Next.
Next. - 20= 0 x + 46US.
Okay.
127 x. Next 254 254 254.
Next 127x= 254. Next x = 254 by 127 cancel.
Okay.
y = - 11x y = - 11 x - 23 by 15 by - 23 by 15 - 45US - 45.
Okay.
X2 Yus 3 question number a x + b yus a + b equal to zero.
B X - A Y - A B = 0.
A X + B YU A + B = 0. So next yus b a xus a x Okay a bus a x bx X - A into Y A into Y A - B - A X by B.
Next - A minus B - A - B = 0. What? B X - A into A A square - - - - - - - - - - - - - - - - - - - - - plus A into B A B - - plus A into A X A² X by B by B next= B² X A² + A B + A² X minus B A into B b²= a minus a cancel a² x + b² square x. Next square a square + b square= a² + b square.
Okay.
square + b square x y = a minus b y = A - B - A X by B. Okay. By B. What? A minus B - A into X.
Okay. - b by bus x yus x + y - a = 0. Next. A x + b y - b² = 0 - b square= 0 x + y= y = a x - Okay.
A x plus b into y a x. Next - b square= 0 - b²= 0. Next. A x + a bxus b²= 0. Next, a xus bus next into b.
Okay.
A minus Bus A plus Hus X - B XUS y = a - x y = a - x a - xus a + Okay.
- b y sa a + b. Okay.
- 3 = 0 3x - 2 y - 10 = 0 Okay.
3 into x 3x - 3 into y - 3 y 10= 0. Okay.
Plus minus okay - 3 y + 2 y - Yusal next y= 0 y x - Y -1 - 3 = 0 X - 4 = 0 X 4 1 3 X + 4 y = 10 next 2x - 2 y = 2.
Okay.
Okay.
3x + 4 y = 10us 4 y.
Okay.
Okay.
7 xal next = 2 into x 2 into - 2 y = 2. Next four 2 - 2 = - 2 y + 2 y 4 2 = 2 y = 2x2 Okay.
2 1 H. Answer.
Next.
3x - 5 y - 4 = 0. Save 9x = 2 y - 2 y - 1 + 1 = 0 9 xus 9 x - 2 y + 1 = 0 plus symbol change - 13 yus.
Next y= y= y = 13 by -3us.
Okay.
9 x - 2 y + 1 = 0 9 x - 2 into y - 1 -1 + 1 = 0 9 x - - + 2 into 1 2 + 1 = 0.
Next to - 1 by 3 is answer. Okay, answer.
Question number 0.4x - 1.5 y = 6.5 next 0.3x + 0.2 2 y = 0.9.4 for 0.4.4 4 into 10 US.5 into 10.5 into 105x 0.2 2.9 Okay, clear.
Okay.
195. Okay. Next.
one plus 12 x - 12 x cancel next - 45 - 8 - 53 - 53 y= 195 36US 159 9 by - 53 53 into 3 159us 3 yus 3x + 2 y 3x + 2 y = 9 3x + 2 into y - 3 into - 2 into - = 9.
Next 3x plus -L= no. Next 3x = nous 3x= xus 3 answer 5us 3 question Number five <unk>2x <unk>3 y=<unk> 5x +<unk> 2 y = 0cept C1 C21 C2 C1 C2 A1 by A2 not equal to the B1 by B2 notice A1 <unk>2 A2<unk> 5 B1 roo<unk>3 B2 <unk>2 Okay C1 C2 zero A1 by A2 not equal to the B1 B2 question A1 by A2 not equal to B2 0.
Okay.
The opposite last number a x + y = x + y - c = Okay.
A x + b y = 0.
a x plus a yus a c = 0. Okay.
US A= Next Bus Aqualus A Cus Bus A= S C by Hus A by A X + b y =0. Next a x + b into y a c by a minus b = z. Next a x plus a b a minus b = z. So next a x = a bus abus next c by a minus b a minus b c by a minus b X - B C by A B A X = B C by B minus A problem X b minus A Y C by A minus B Clear.
First question.
X + 2 Y + 1 = 0. Say 2X - 3 Y - 12= 0.
X 1 B1 Y 2 C1 A2 B2 Yus 3 C2 -2 X B1 C2 B2 - B2 C1 = Y by C1 A2 - C2 A1 = 1 by A1 B2 minus A2 B1 Okay by 2 into C2 Next minus B2 B2 - 3 - 3 into C1 C1 into 1 equal to Y by next C1 into A2 A2 A2 minus C2 C2 - 12 AUS C2 into A1 A1 1 = 1 by A1 A1 B2US A2 A2 into B1 B1 2 next by 2 into -= Y by -= 1 I 1 into - 3 - 3 - x + = y by = 1 - Okay. Next. XY - X by -= last 1 by - 7 1 by - 7 - 7 X= 1 - cancel X.
Okay.
Y 14 = 1 by - 7 - 7 y = 14 y 14 by - 7 - 3 - 2 2x + 5 y = 1 2x + 3 y = 3 a1 B1 C1 A2 B2 C2.
Okay. Say formula x by b1 c2 minus b2 c1 = y by c1 a2 minus c2 a1 = 1 by a1 b2 minus a2 b1 x by b1 5 into c2 - 3us okay b2 C2 3 into C1 -1 = Y by Y by C1 or -1 into A2 - C2 C2 - 3 - 3 into A1 2 = 1 by 1 by A1 A1 2 into B2 A2 3 - A2 into B1 XUS plus Y - 1 into 2 - 2 - - - plus.
Okay. + 6 = 1 by = y by - 2 + 6 = 1 by 6 - 10 - 4 - 4 x -2= 1 by - 4 - cancel x= 4x= okay 4x= 4x 4x= Next 4 = 1 by - 4 - 4 y = 4 y = 4 by - 4 -1. Okay. Answer 31.
Okay.
Question number x + 6 y + 1 = 0. Say 2x + 3 y + 8 = 0.
A1 C1 A2 B2 C2 X by B1 C2 minus B2 C1 = Y by C1 A2 minus C2 A1 = 1 by A1 B2 - A2 B1 X by B1 6 into C2 8 - B2 B2 B2 into C1 1 = Y by C1 into A2 minus C2 8 into A1 = 1 by a1 into b2 3 - a2 2 into b1 6 Okay= y 2us - 8 - 6 - 6 = 1 by 3 - 12 - 9 - 9 x 45= 1 by - 9 - 9 x = 45 x 45 - 9 - 5 x - 5 y - 6 = 1 - 9 - 9 y = - 6 into 1 - 6 - - cancel y 6 by 9 by 3 Okay, y 2x3 Okay.
Question number four.
X + Y by B. Okay. X by A + Y by Bal A + B a + X by A² X by A² + Y by square = 2 X a square + B square= 2 Okay.
A 1 by a 1 by a x by a 1 by a x.
Okay.
1 A 1 A B 1 by C1.
Okay.
B1 A² sorry A1 sorry A2 okay A2 A2 next square X by b1 c2 - b2 c1 = y by c1 a2 - c2 a1 = 1 by a1 b2 minus a2 b1 okay formula x1 b into c2 - 2 - b2 1 by b² into c1 c1 - into a + b. Okay.
Next = y by c1 - into a + b into a2 1 by a² minus c2 - 2 into a1 a1 a1 by a. Okay. equal to 1 by A1 A1 by A into B2 B2 1x B² minus A2 a2 1x A² into B1 b1 B okay next by 1 into - 2 - 2 - 2 by - 1 into a + a + b square. Okay. = y byus into a b a + b - a - b a square a squareus 2 into a 2 into 1 2 2 by a = 1 by 1 into 1 1 a² a b² - 1 into 1 1 a² b a square b next x b square plus b square b square a + b a + b = y by a square A square a into 2 a. Okay.
The next 1 square Okay. A square B square B square A square A into 1 A minus A square B A square next step Next.
Okay.
X A to - 2 B + B - B - 2 B + B - B - B square B square next = Y by Y by 2 A 2 A A a b a - b a square = 1 a - b by a square b square a - b by a square b square by square 1 by a - b by a² b² square. Next into a square b² = 1 into a - b by b² a - b by b² into a square b x a² x + a² by a² b² = 1 into a - b by a² square y = a - b by a² into a² b² by a minus b a b a square a square y b square y square a square b square question Number five.
Okay.
Next number.
Next number.
Same question.
Question 4x - 9 y = 3x + 2 y - 35 = 0. Okay. A1 A2 B2 C2US.3 C. Okay.
Formula X by B1 C2 minus B2 C1 = Y by C1 A2 - C2 A1 = 1 by A1 B2 - A2 B1 Okay X by B1 B1 - 9 into C2 -.3 C -.3 C minus B2 into C1 C1 0.
Okay. = y by c1 0 to 0 into a2 a2 minus c2 minus.3 c into a1 a1 equal to 1 by a1 into b2 a2 a into b1us no XUS equal to Y by -= 1 byus 35 35.
Next xal 1 by 3 1 by 35 35 x = x= y 140 y by 140 = 1 by 35 35 y = 140 y 140 by 35.
Y question number foreign.
First question x + 3 by y = 17. Next 1x + 1 by y = 7.
Okay.
2x + 3x y = 17. Next 1 by x + 1 by y 1 by Okay.
1 2 1 by 2 1 into 2 1 by 2 x 1 x 2 by x U okay next 3x yal Okay.
U 3 B = 17. A 2 into U. 2 U H plus 2 into V 2 V next= 14. Okay.
2 U - 2 U 3 B - 2 B plus B.
= 7. U + = 7.
U= next. U= 1x= Okay.
Next 1x = 4x is 1 1 into 1 1 x = 1 by 4 x value 1 y = 1 into 1 Y= 1 by 4 1 by 3.
Question number two + 6 y = 13. Say next 3x + 20 y = 35.
X 85 X 83 by Okay.
15 by X plus 189 into 3 15 by =.3.
Okay. 175us 18 yus 100 yus 82 y next equal to minus 175 39us 175 39us Nextus y= 136 by 82 82.
Okay. Y 68 by 41.
Okay. Next.
Okay.
5 by X + 6 into Y. Y 68 by 41. Okay.
41= 13. So next 5 byal 5x 5 by x = 13us 5x = 41 41 into Okay.
Okay. 53us 41 into 1 41 1.
Next 5 by = 923.
Okay.
Next 125= Next.
Okay.
41 by 25 41 by 25 Yam 68 by 41 something 68 by 41 68 by 41 answer.
Next question number three.
Okay.
Number 2X - 3 y = 9. Say 3x + 7 y = 2. Okay. X cancel.
6xus 9 by yal.
Okayus - 9 by y -4 by y = 27 - 4 23 y - 9 -4 = 23. Next step -4 - 9 - 23 - 23 by y = 23. So next step y into 23 23 y 1 into - 23 - 23 y = - 23 by 23us 2xus - 3x y - 9 2x - 9 + 3us 2x = x = 3us 1 number 4x + 6 y = 3x y 8 x + 9 Y = 5 X Y Okay.
Next solve 4xy + 6 y by xy = 3xy by xy.
Left side. Right side y 6 by x + 4 by y = 3.
Okay.
8 x 8 x by xy + 9 y by xy = 5 xy by xy x 8 y xy 5 y = Okay.
Okay.
Okay.
6 by 4 by y = 3. 4 by y = 3.
9x + 8 y 9 by x + 8 by y= 5= 5 Okay.
Okay.
8 by Okay. Next 8 by Y = 5. Okay.
Y 12 by X - 9 by X 6 - 5. So next 12 - 9 12 - 9 by Next.
Okay.
9 by + 8 by y = 5.
9 by 9 by 3 + 8 by y = 5. Next 8 by = 5. Next 8 y= 2 y = y = question Number five.
minus.
Okay.
A + yus b a - b into x - a + b into x. Next equal plus a square - a square cancel 2 a - b square - b square - 2 b² x a - b - a - balus 2 - 2 plus minus okay - 2 bx = - 2 b into a + b X Ara.
Okay.
Okay.
A + B A + B into X A + B. Okay. A + B. Next. Plus a + b into y = a² + b² a square + b square into a + a square.
A + square formula a² + 2 a + b² a + b into y = a² + b².
Next A + B into Y= 2 A Y a + b a + b comma - 2 a b by a + b.
Okay. Answer question number five.
Question number six.
Question number six. X by A + Y by B = A XUS A X - B YUS B Y = A² - B square A square - B square A B B A Yal 2. Next, bx + a y = 2 a 2 a x - b y = a² - b² B into B X B² X A Y into B A B Y plus Okay equal to 2 A B into B 2 A B² 2 A B² next a A² X minus A B Y= A into A² A minus A into B square A square. Okay.
Next. B² X + A² X = A A 2 A square root A square 2 A square roo<unk> 1 A square A square A square A square. Next b² a² + b square = a square b square Next to a into x a squareus y = a² b² a square a square next b y = - b square - y = b² by b So okay answer a Y A question number seven.
Question number seven.
1 by y + y - y 1 x + y u 1 = z 15 u + 7 B - 10 = 0.
Okay.
15= 0 15 U + 7 B - 10 =US plusal Next 13 by 13.
Next 15 U - 6 V + 3 = 0 15 B 15 U - 6 into B 6 plus 3 = 0 next 15 U - 6 + 3 - 3 = 0 15 U= Okay. 1x.
Okay.
U 1 x + y 1 x - y 1x + yal 1x 5 1 x + y into 1 x + y = 5 into 1 1 x - y Okay, x - y into 1 x - y 1% Okay.
x + y = 5 x - y = 1 + y - yal Next.
Okay.
x + y = x 3 + y 3 + y = 5 y question Number eight.
X Y by X + Y = 6 by 5. Say x y - x = 6 + y.
Okay.
Next xy xy + y by xy = 5 by 6 x 1x y 1x = 5 by 6. So 1x + 1 by y = 5 by 6 y by xy - xy = 1 by 6 y x 1x y= 1 by 6. Okay.
1x + 1 y = 5 by 6 5 by 6 1x - 1 by y = = 1 by 6 1 by 6 + 1 y - 1 by y 1x X + 1 by X = 5X 6 + 1 by 6 5 + 1 2 X= Okay, next into X= 2 X 1 by X 1 by 2 + 1 by Y = 5 by 6 1X Y = 5 by 6 - 1 by 2 1 by Y Next.
Next. 2 into 2 y= Okay.
Question number.
Okay. First 6x + 5 y = 7 x + 3 y + 1.
Okay.
Right.
6 3 y 5 y - 5 y + 1 = 0. Next 7 x - 6 3 y - 5 y - 2 y + 1 = 0.
Say next one. 7 x + 3 y + 1 = 2 into x 2x + 12 yus 7 x 2x - 2x + 3 y 12 y - 12 y + 1 - 2 + 2 = 0. Next 7 x 2 5 x 3 y - 12 y - 9 y 1 + 2 3 = 0. Okay.
x - 2 y + 1 = 0 5 x - 9 y + 3 = 0.
5 into x 5 x - 10 y + 5us 9 y.
Okay.
- + - 10 y + 9 y - y Okay 5 - 3 + 2 + 2 = next = - y = 2 x - 2 into y= next. X - 2 into 2 - 4 - 4 + 1 - 3 = 0 X= N.
Okay.
x + y - 8 by 2 = x + 2 y -4 by 3.
3 into 3 into x + y - 8 = 2 into x + 2 y - 14. Next 3 into x 3x + 3 into y 3 yus 2 into x 2x 4 yus.
Okay 3x 2x - 2x + 3 y 4 y - 4 y -4 + 28 + 28 = 0. Next 3x 2x 3 y - 4 y - yus = 3 = 3x + y - 12 by 11. Okay. x + Okay.
US equal 9x + 3 into y 3 yus what next 11 x - 9 x + 22 y - 3 y - 154 + 36 = 0 2x X by C minus 19 X.
Okay.
Okay.
X - Y X - Y + 4. Now Yes. + 4 = 2X + 19 Y. 2X + 19 Y. Nextusal 2= 2x + 19 yusal.
Okay.US plus - 2 y - 19 - 21 y - 21 y plus 126 = 0.
Next - 21 y = 126 y = 126 by Okay.
Next.
Okay. X - Y + = 0. X Y X - Y 6 + 4 = X - 6 + 4 - 2 = 0. X + 2 answer number 11 X + Y by 2 - X - Y by 3= 8. Okay.
Yus 2 into x - y = 8. The next stage 3 into x 3x + 3 into y 3 y - 2 into x 2x - - + 2 into y 2 yal 3x - 2x 3 y + 2 y= x + y by 3 + x - y by 4 = 11 into x + y 3 into x - y = next 4 into x 4x + 4 into y 4 y + 3 into x 3x - 3 into y 3 Next 4x + 3x 7 x 4 y - 3 y + y= x + 5 y x + 5 y - = No, say I'm going to do is 7 x + y 7 x + y next So the X.3 C YUS 33 Okay y US equal.3 y.3 y - 1 y 34 34 yus next 34 yal Y= 34. Okay.
Okay.
Okay.
Next x + 5 into yus 48 = 0. Now, xdus x tusal.
Okay.
Number x= yal a y. Next step= a x + b y = a² + b² = a x + b y = a² + b² y Okay.
B² XUS A Y = B into a A² X + A B Y = A into A² A + A into B square A square B² X + A² X = a² + 8 b² next a² + b square a² + b square = a into a square + b square a square + b square x A okay a yus a y =0 next a y= aus y = a by a a Y B A Y B Answer A B Okay, clear number.
Okay.
Okay.
HC 2.0 YouTube channel.
Okay.
Okay.
Number five.
Question number five.
Answer us.
Next number 2us.
Next number 0 5 4us 0us answer. Okay. Number 1 by 2 3x 4 1 1 by 5. Okay. So 1 by 2 into 1x 5 - 3x 4 into 1us Answer six number 2x + 3 y = 5x + y = 4 a1 A2 B2 C2us.
Okay.
x.
Okay.
L formula A1 A2 B1 B2 B1 B2 - C1 - C2 Y A1 A2 - C1 - C2 A B1 B2 - C1US C1US plus C2us B1 B1 B2.
Okay.
5 - 12 - 7 - 7 next. A1 A1 A2.
Okay.
X.
Okay.
1 answer number x + y = 3 2x + 3 y = 8 A1 B1 C1US A2 B2 C2 first A1 A2 B1 B2 A1 1 A 2 B1U D X B1 B2 C1 C2 C1us AUS B1 B2 1 Now 1 Y A1 A2 - C1 - C2 A1 A A1 A2 C1US C1 Okay.
Okay. Next y by del y 2 2 by a 2 by 1 answer 1 2 answer 1 2 = 2x + y = 3 A1 X 1 B1 minus one C1 Z A2 B2 virus 1 C2 A1 A2 B1 B2 A1 A2 B1 get minus1 B2 get 1 - 2 into -1 - 2 - okay x b1 b2 - c1us c2us1us2 - b1 -1 b2 3 into + Okay. Say next. Y A1 A2 - C1 - C2 A1 A2us C1US C2 Okay X by Xin Y Okay.
2x - y = 3. Say x - 3 y = -1.
Am B1 C1 - 3US A2 1 B2 - 3 C2 -1 A1 A2 B1 B2 A1 A2 A B1 A minus A B2 -3 2 into -3 - 6 - 1 into -1 -1 - - plus - next del x d x b1 b2 - c1 - c21us plus c2 aus b1 b1us B2 B2 - 3 - 3 to 3 into - 3 - 9 - Y A1 A2 - C1 - C2 A1 A1 2 A2 1 - C1 - A Okay. 2 into - x = d x by d xus y by del yus by Question number one question number six number.
Okay.
Next video.
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