Question

Solve the following pairs of liner equation by the method of substitution:
$x+y=7,3x-y=1$

Answer 1

We know that, for a pair of linear equation:

$a_{1}x+b_{1}x+c_1=0$

$a_{2}x+b_{2}x+c_2=0$

Has no solution if

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Here:- $2x-3y=5$

$2x=3y=7$

$\frac{a_1}{a_2}=\frac{2}{2}=\frac{1}{1};\frac{b_1}{b_2}=\frac{3}{3};\frac{c_1}{c_2}=\frac{5}{7}$

Since $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$, so given equation has no solution.