Answer
$(6,17)$
Work Step by Step
The given system of equations is
$\Rightarrow 2x-y=-5$ ...... (1)
$\Rightarrow 3x-y=1$ ...... (2)
Solve for $y$ in equation (2).
$\Rightarrow 3x-y=1$
$\Rightarrow 3x=1+y$
$\Rightarrow 3x-1=y$ ...... (3)
Substitute $3x-1$ for $y$ in equation (1).
$\Rightarrow 2x-(3x-1)=-5$
Clear the parentheses.
$\Rightarrow 2x-3x+1=-5$
Add like terms.
$\Rightarrow -x+1=-5$
Add $x+5$ to each side.
$\Rightarrow -x+1+x+5=-5+x+5$
Simplify.
$\Rightarrow 6=x$
Substitute $6$ for $x$ in equation (3).
$\Rightarrow y=3(6)-1$
Simplify.
$\Rightarrow y=18-1$
$\Rightarrow y=17$
Check
Equation (1)
$\Rightarrow 2x-y=-5$
$\Rightarrow 2(6)-(17)=-5$
$\Rightarrow 12-17=-5$
$\Rightarrow -5=-5$
True.
Check
Equation (2)
$\Rightarrow 3x-y=1$
$\Rightarrow 3(6)-(17)=1$
$\Rightarrow 18-17=1$
$\Rightarrow 1=1$
True.
Hence, the solution is $(6,17)$.
