## RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.8
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.9
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.10
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.11
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables VSAQS
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables MCQS

**Solve the following systems of equations:**

**Question 1.**

11x + 15y + 23 = 0

7x – 2y – 20 = 0

**Solution:**

11x + 15y + 23 = 0 => 11x + 15y = -23 ……..(i)

7x – 2y – 20 = 0 => 7x – 2y = 20 ……….(ii)

Multiply (i) by 2 and (ii) 15, we get

22x + 30y = -46

105x – 30y = 300

Adding we get

127x = 254 => x = \(\frac { 254 }{ 127 }\) = 2

7 x 2 – 2y = 20 => 14 – 2y = 20

-2y = 20 – 14 = 6

y = -3

**Question 2.**

3x – 7y + 10 = 0

y – 2x – 3 = 0

**Solution:**

**Question 3.**

0.4x + 0.3y = 1.7

0.7x – 0.2y = 0.8

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

7(y + 3) – 2(x + 2) = 14

4(y – 2) + 3(x – 3) = 2

**Solution:**

**Question 6.**

\(\frac { x }{ 7 } +\frac { y }{ 3 } =5\)

\(\frac { x }{ 2 } -\frac { y }{ 9 } =6\)

**Solution:**

**Question 7.**

\(\frac { x }{ 3 } +\frac { y }{ 4 } = 11\)

\(\frac { 5x }{ 6 } -\frac { y }{ 3 } = -7\)

**Solution:**

**Question 8.**

\(\frac { 4 }{ x }\) + 3y = 8

\(\frac { 6 }{ x }\) – 4y = -5

**Solution:**

**Question 9.**

x + \(\frac { y }{ 2 }\) = 4

\(\frac { x }{ 3 }\) + 2y = 5

**Solution:**

**Question 10.**

x + 2y = \(\frac { 3 }{ 2 }\)

2x + y = \(\frac { 3 }{ 2 }\)

**Solution:**

**Question 11.**

√2x – √3y = 0

√3x – √8y = 0

**Solution:**

**Question 12.**

3x – \(\frac { y + 7 }{ 11 }\) + 2 = 10

2y + \(\frac { y + 11 }{ 7 }\) = 10

**Solution:**

**Question 13.**

2x – \(\frac { 3 }{ y }\) = 9

3x + \(\frac { 7 }{ y }\) = 2, y ≠ 0

**Solution:**

Hence x = 3, y = -1

**Question 14.**

0.3x + 0.7y = 0.74

0.3x + 0.5y = 0.5

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

**Solution:**

**Question 21.**

**Solution:**

**Question 22.**

**Solution:**

**Question 23.**

**Solution:**

**Question 24.**

**Solution:**

**Question 25.**

**Solution:**

**Question 26.**

**Solution:**

**Question 27.**

**Solution:**

**Question 28.**

**Solution:**

**Question 29.**

**Solution:**

**Question 30.**

**Solution:**

**Question 31.**

**Solution:**

**Question 32.**

**Solution:**

**Question 33.**

**Solution:**

**Question 34.**

x + y = 5xy

3x + 2y = 13xy

**Solution:**

**Question 35.**

**Solution:**

**Question 36.**

2 (3u – v) = 5uv

2 (u + 3v) = 5uv

**Solution:**

**Question 37.**

**Solution:**

**Question 38.**

**Solution:**

**Question 39.**

**Solution:**

**Question 40.**

**Solution:**

**Question 41.**

**Solution:**

**Question 42.**

**Solution:**

**Question 43.**

152x – 378y = -74

– 378x + 152y = -604

**Solution:**

152x – 378y = -74 ……..(i)

– 378x + 152y = -604 ………(ii)

Adding (i) and (ii), we get

– 226x – 226y = 678

Dividing by -226,

x + y = 3 ……..(iiii)

and subtracting (ii) from (i)

530x – 530y = 530

Dividing by 530,

x – y = 1 ……..(iv)

Adding (iii) and (iv)

2x = 4

x = 2

From (iii), 2 + y = 3

y = 3 – 2 = 1

Hence x = 2, y = 1

**Question 44.**

99x + 101y = 499

101x + 99y = 501

**Solution:**

99x + 101 y = 499 ….(i)

101x + 99y = 501 ……(ii)

Adding we get

200x + 200y = 1000

x + y = 5 ……(iii)

(Dividing by 200)

Subtracting we get

-2x + 2y = -2

=> x – y = 1 ….(iv)

(Dividing by -2)

Now adding (iii) and (iv)

2x = 6 => x = 3

and subtracting (iv) from (iii)

2y = 4 => y = 2

Hence x = 3, y = 2

**Question 45.**

23x – 29y = 98

29x – 23y = 110

**Solution:**

23x – 29y = 98 ….(i)

29x – 23y = 110 ….(ii)

Adding (i) and (ii) we get

52x – 52y = 208

x – y = 4 ….(iii)

(Dividing by 52)

Subtracting (ii) from (i)

6x + 6y = 12

=> x + y = 2 ….(iv)

(Dividing by 6)

Adding (iii) and (iv)

2x = 6 => x = 3

Subtracting (iv) from (iii)

2y = -2 => y = -1

Hence x = 3, y = -1

**Question 46.**

x – y + z = 4

x – 2y – 2z = 9

2x + y + 3z = 1

**Solution:**

x – y + z = 4 ……(i)

x – 2y – 2z = 9 ……(ii)

2x + y + 3z = 1 ……(iii)

**Question 47.**

x – y + z = 4

x + y + z = 2

2x + y – 3z = 0

**Solution:**

x – y + z = 4 ….(i)

x + y + z = 2 ….(ii)

2x + y – 3z = 0 ….(iii)

From (i)

z = 4 – x + y

Substituting the values of z in (ii) and (iii)

x + y + 4 – x + y = 2

2y = 2 – 4 = -2

y = -1

and 2x + y – 3(4 – x + y) = O

2x + y – 12 + 3x – 3y = 0

5x – 2y = 12

5x – 2(-1) = 12

5x + 2 = 12

5x = 12 – 2 = 10

x = 2

From (i),

2 – (-1) + z = 4

2 + 1 + z = 4

3 + z = 4

z = 4 – 3 = 1

Hence x = 2, y = 1, z = 1

**Question 48.**

21x + 47y = 110

47x + 21y = 162

**Solution:**

We have,

21x + 47y = 110 …(i)

47x + 21y = 162 …(ii)

Multiplying equation (i) by 47 and Equation (ii) by 21, we get

987x + 2209y = 5170 …(iii)

987x + 441y = 3402 …(iv)

Subtracting equation (iv) from equation (iii),

we get

1768y = 1768

y = 1

Substituting value of y in equation (i), we get

21x + 47 = 110

or 21x = 63

or x = 3

So, x = 3, y = 1

**Question 49.**

If x + 1 is a factor of 2x^{3} + ax^{2} + 2bx + 1, then find the values of a and b given that 2a – 3b = 4

**Solution:**

**Question 50.**

**Solution:**

**Question 51.**

Find the values of x and y in the following rectangle

**Solution:**

Hence, the required values of x and y are 1 and 4, respectively.

**Question 52.**

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x – y = 1. How many such lines can we find?

**Solution:**

Plotting the points A (2, 0) and B (0, 2), we get the straight line AB. Plotting the points C (0, -1) and D (\(\frac { 1 }{ 2 }\) , 0) we get the straight line CD. The lines AB and CD intersect at E (1, 1).

Hence, infinite lines can pass through the intersection point of linear equations x + y = 2 and 2x – y = 1

¡.e.,E(1, 1) like as y = x, 2x + y = 3, x + 2y = 3, so on.

**Question 53.**

Write a pair of linear equations which has the unique solution x = -1, y = 3. How many such pairs can you write?

**Solution:**

Hope given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 are helpful to complete your math homework.

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