Question

Solve the following system of linear equations by using the method of substitution:
$2x-3y=2,x+2y=8$

Answer 1

Given
$2x-3y=\mathrm{2...}\left(1\right)$
$x+2y=\mathrm{8....}\left(2\right)$

From (2), we have,
x = 8 - 2y

Substituting this value of x in (1), we have,
2(8 - 2y) - 3y = 2
i.e., 16 - 4y - 3y = 2 $\Rightarrow$ 7y = 14
$\Rightarrow y=2$

Now, x = 8 - 2y $\Rightarrow$ x = 8 - 2(2) = 4
Thus, x = 4 and y = 2