Question

Solve the following systems of equations and investigate them with respect to $a$.
$2x+3y=5,x-y=2,x+4y=a$

Answer 1

Given equations,

$2x+3y=5\to \left(1\right)$

$x-y=2\to \left(2\right)$

$x+4y=a\to \left(3\right)$

$\left(3\right)-\left(2\right(\Rightarrow 5y=a-2$

$y=\frac{a-2}{5}$

$x=2+y\Rightarrow x=\frac{8+a}{5}$

$2x+3y=5\Rightarrow \frac{16+2a+3a-6}{5}=5$

$a+2=5$

$a=3$

$y=\frac{1}{5},x=\frac{11}{5}$

$x+4y=\frac{11}{5}+\frac{4}{5}=\frac{15}{5}=3=a$ (proved)

$x=\frac{11}{5},y=\frac{1}{5}$ is solution of given equations.