Answer
$(-2,-\frac{9}{2})$
Work Step by Step
The given system of equations is
$\Rightarrow x-2y=7$ ...... (1)
$\Rightarrow 3x-2y=3$ ...... (2)
Solve for $x$ in equation (1).
$\Rightarrow x-2y=7$
$\Rightarrow x=7+2y$ ...... (3)
Substitute $7+2y$ for $x$ in equation (2).
$\Rightarrow 3(7+2y)-2y=3$
Clear the parentheses.
$\Rightarrow 21+6y-2y=3$
Add like terms.
$\Rightarrow 21+4y=3$
Subtract $21$ from each side.
$\Rightarrow 21+4y-21=3-21$
Simplify.
$\Rightarrow 4y=-18$
Divide each side by $4$
$\Rightarrow \frac{4y}{4}=\frac{-18}{4}$
Simplify.
$\Rightarrow y=-\frac{9}{2}$
Substitute $-\frac{9}{2}$ for $y$ in equation (3).
$\Rightarrow x=7+2(-\frac{9}{2})$
Clear the parentheses.
$\Rightarrow x=7-9$
Simplify.
$\Rightarrow x=-2$
Check
Equation (1)
$\Rightarrow x-2y=7$
$\Rightarrow -2-2(-\frac{9}{2})=7$
$\Rightarrow -2+9=7$
$\Rightarrow 7=7$
True.
Check
Equation (2)
$\Rightarrow 3x-2y=3$
$\Rightarrow 3(-2)-2(-\frac{9}{2})=3$
$\Rightarrow -6+9=3$
$\Rightarrow 3=3$
True.
Hence, the solution is $(-2,-\frac{9}{2})$.
