Question

solve the following pair of linear equations. 3 X + 4 Y = 10 and 2x - 2y = 2​

Answer 1

3x + 4y = 10 and 2x – 2y = 2

By elimination method

3x + 4y = 10 .... (i)

2x – 2y = 2 ... (ii)

Multiplying equation (ii) by 2, we get

4x – 4y = 4 ... (iii)

3x + 4y = 10 ... (i)

Adding equation (i) and (iii), we get

7x + 0 = 14

Dividing both side by 7, we get

x = 14/7 = 2

Putting in equation (i), we get

3x + 4y = 10

3(2) + 4y = 10

6 + 4y = 10

4y = 10 – 6

4y = 4

y = 4/4 = 1

Hence, answer is x = 2, y = 1

By substitution method

3x + 4y = 10 ... (i)

Subtract 3x both side, we get

4y = 10 – 3x

Divide by 4 we get

y = (10 - 3x )/4

Putting this value in equation (ii), we get

2x – 2y = 2 ... (i)

2x – 2(10 - 3x )/4) = 2

Multiply by 4 we get

8x - 2(10 – 3x) = 8

8x - 20 + 6x = 8

14x = 28

x = 28/14 = 2

y = (10 - 3x)/4

y = 4/4 = 1

Hence, answer is x = 2, y = 1 again.

Answer 2

3X+4Y=10.

2X-2Y=2. ×2

3X+4Y=10

4X-4Y=4

----------------

=7X. =14

=X=14/7

=X=2

2X-2Y=2

2(2)-2Y=2

4-2Y=2

-2Y=2-4

-2Y=-2

Y=-2/-2

Y=1

X=2;Y=1