Question

Question 1 (ii)
Solve the following pair of linear equations by the elimination method and the substitution method:
3x + 4y = 10 and 2x - 2y = 2

Answer 1

The given equations are

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
$x=\frac{14}{7}=2$
Putting in equation (i), we get
3x + 4y = 10
3(2) + 4y = 10
6 + 4y = 10
4y = 10 - 6
4y = 4
$y=\frac{4}{4}=1$
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
$y=\frac{(10-3x)}{4}$
Putting this value in equation (ii), we get
2x - 2y = 2 ... (ii)
$2x-\frac{2(10-3x)}{4}=2$
Multiply by 4 we get
8x - 2(10 - 3x) = 8
8x - 20 + 6x = 8
14x = 28
$x=\frac{28}{14}=2$
$y=\frac{10-3x}{4}$
$y=\frac{4}{4}=1$
Hence, answer is x = 2, y = 1 again.