Question

Solve the following pairs of liner equation by the method of substitution:
$x-y=3,3x-3y+=9$

Answer 1

We know that, a pair of linear equation

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

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

Has infinitely many solutions if

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

Here :- $x-y=3$

$3x-3y=9$

$\frac{a_1}{a_2}=\frac{1}{3};\frac{b_1}{b_2}=\frac{1}{3};\frac{c_1}{c_2}=\frac{3}{9}=\frac{1}{3}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=\frac{1}{3}$

System has infinitely many solution and can calculated using only one equation by putting the value of one variable of own choice.

$x-y=3$

Put $x=1\to y=x+3=2+3=4$

$x=1,y=4$