Answer
$(-1,1)$
Work Step by Step
The given system of equations is
$\Rightarrow x=6y-7$ ...... (1)
$\Rightarrow 4x+y=-3$ ...... (2)
Substitute $6y-7$ for $x$ in equation (2).
$\Rightarrow 4(6y-7)+y=-3$
Use distributive property.
$\Rightarrow 24y-28+y=-3$
Add like terms.
$\Rightarrow 25y-28=-3$
Add $28$ to each side.
$\Rightarrow 25y-28+28=-3+28$
Simplify.
$\Rightarrow 25y=25$
Divide each side by $25$.
$\Rightarrow \frac{25y}{25}=\frac{25}{25}$
Simplify.
$\Rightarrow y=1$
Substitute $1$ for $y$ in equation (1).
$\Rightarrow x=6(1)-7$
Simplify.
$\Rightarrow x=6-7$
$\Rightarrow x=-1$
Check
Equation (1)
$\Rightarrow x=6y-7$
$\Rightarrow -1=6(1)-7$
$\Rightarrow -1=6-7$
$\Rightarrow -1=-1$
True.
Check
Equation (2)
$\Rightarrow 4x+y=-3$
$\Rightarrow 4(-1)+1=-3$
$\Rightarrow -4+1=-3$
$\Rightarrow -3=-3$
True.
Hence, the solution is $(-1,1)$.
