Answer
The solution is $(1,-3)$.
Work Step by Step
The given system of equations is
$\Rightarrow 6x-9=y$ ...... (1)
$\Rightarrow y=-3x$ ...... (2)
Substitute $-3x$ for $y$ in equation (1).
$\Rightarrow 6x-9=-3x$
Add $3x+9$ to each side.
$\Rightarrow 6x-9+3x+9=-3x+3x+9$
Simplify.
$\Rightarrow 9x=9$
Divide each side by $9$.
$\Rightarrow \frac{9x}{9}=\frac{9}{9}$
Simplify.
$\Rightarrow x=1$
Substitute $1$ for $x$ in equation (2).
$\Rightarrow y=-3(1)$
Simplify.
$\Rightarrow y=-3$
Check
Equation (1)
$\Rightarrow 6x-9=y$
$\Rightarrow 6(1)-9=-3$
$\Rightarrow 6-9=-3$
$\Rightarrow -3=-3$
True.
Check
Equation (2)
$\Rightarrow y=-3x$
$\Rightarrow -3=-3(1)$
$\Rightarrow -3=-3$
True.
Hence, the solution is $(1,-3)$.
