Answer
No solution.
Work Step by Step
First equation $2x-3y=6$.
Plug $y=0$ into the equation.
$\Rightarrow 2x-3(0)=6$
$\Rightarrow 2x=6$
$\Rightarrow \frac{2x}{2}=\frac{6}{2}$
$\Rightarrow x=3$
$x−$ intercept $A=(3,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 2(0)-3y=6$
$\Rightarrow -3y=6$
$\Rightarrow \frac{-3y}{-3}=\frac{6}{-3}$
$\Rightarrow y=-2$
$y−$ intercept $B=(0,-2)$.
Second equation $4x-6y=24$.
Plug $y=0$ into the equation.
$\Rightarrow 4x-6(0)=24$
$\Rightarrow 4x=24$
$\Rightarrow \frac{4x}{4}=\frac{24}{4}$
$\Rightarrow x=6$
$x−$ intercept $A=(6,0)$.
Plug $x=0$ into the equation.
$\Rightarrow 4(0)-6y=24$
$\Rightarrow -6y=24$
$\Rightarrow \frac{-6y}{-6}=\frac{24}{-6}$
$\Rightarrow y=-4$
$y−$ intercept $B=(0,-4)$.
Draw two lines using intercept points.
Both lines are parallel.
Hence, we have no solution.