Answer
$\{(x,y)|3x-2y=6\}$ or $\{(x,y)|6x-4y=12\}$.
Work Step by Step
First equation $3x-2y=6$.
Plug $y=0$ into the equation.
$\Rightarrow 3x-2(0)=6$
$\Rightarrow 3x=6$
$\Rightarrow \frac{3x}{3}={6}{3}$
$\Rightarrow x=2$
$x−$ intercept is $A=(2,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 3(0)-2y=6$
$\Rightarrow -2y=6$
$\Rightarrow \frac{-2y}{-2}=\frac{6}{-2}$
$\Rightarrow y=-3$
$y−$ intercept $B=(0,-3)$.
Second equation $6x-4y=12$.
Plug $y=0$ into the equation.
$\Rightarrow 6x-4(0)=12$
$\Rightarrow 6x=12$
$\Rightarrow \frac{6x}{6}=\frac{12}{6}$
$\Rightarrow x=2$
$x−$ intercept $C=(2,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 6(0)-4y=12$
$\Rightarrow -4y=12$
$\Rightarrow \frac{-4y}{-4}=\frac{12}{-4}$
$\Rightarrow y=-3$
$y−$ intercept $D=(0,-3)$.
Both lines are coincident.
Hence, the system has infinitely many solutions.
The solution set is
$\{(x,y)|3x-2y=6\}$ or $\{(x,y)|6x-4y=12\}$.
