Answer
$(\frac{1}{2},-\frac{3}{4})$
Work Step by Step
The given system of equations is
$\Rightarrow 3x+2y=0$ ...... (1)
$\Rightarrow y=\frac{1}{2}x-1$ ...... (2)
Substitute $\frac{1}{2}x-1$ for $y$ in equation (1).
$\Rightarrow 3x+2(\frac{1}{2}x-1)=0$
Use distributive property.
$\Rightarrow 3x+x-2=0$
Add like terms.
$\Rightarrow 4x-2=0$
Add $2$ to each side.
$\Rightarrow 4x-2+2=0+2$
Simplify.
$\Rightarrow 4x=2$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{2}{4}$
Simplify.
$\Rightarrow x=\frac{1}{2}$
Substitute $\frac{1}{2}$ for $x$ in equation (2).
$\Rightarrow y=\frac{1}{2}(\frac{1}{2})-1$
Simplify.
$\Rightarrow y=\frac{1}{4}-1$
Add fraction.
$\Rightarrow y=\frac{1-4}{4}$
Simplify.
$\Rightarrow y=-\frac{3}{4}$
Check
Equation (1)
$\Rightarrow 3x+2y=0$
$\Rightarrow 3(\frac{1}{2})+2(-\frac{3}{4})=0$
$\Rightarrow \frac{3}{2}-\frac{3}{2}=0$
$\Rightarrow 0=0$
True.
Check
Equation (2)
$\Rightarrow y=\frac{1}{2}x-1$
$\Rightarrow -\frac{3}{4}=\frac{1}{2}(\frac{1}{2})-1$
$\Rightarrow -\frac{3}{4}=\frac{1}{4}-1$
$\Rightarrow -\frac{3}{4}=\frac{1-4}{4}$
$\Rightarrow -\frac{3}{4}=-\frac{3}{4}$
True.
Hence, the solution is $(\frac{1}{2},-\frac{3}{4})$.
