Answer
$x=6$
$y=-4$
Work Step by Step
1st. Rewrite both equations in the form of Ax+By=C. first arrange the system so that variable terms appear on the left and constants appear on the right.
2nd. If necessary, multiply either equation or both equations by appropriate numbers so that the sum of the x-coefficients or the sum of the y-coefficients is $0$. eliminate $x$ or $y$.
3rd.Add the equations
4th.Solve the equations in one variable
5th.Back-Substitute and find the value for the other variable
6th.Check
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For example, let's take $3x+5y=-2$ and $2x+3y=0$
1st.
{ $3x+5y=-2$
{ $2x+3y=0$
2nd.
let's multiply the second equation by $-3/2$ to eliminate the $x$
{ $3x+5y=-2$
$-3/2$ { $2x+3y=0$, the second equation will be, $-3x-9y/2=0$.
{ $3x+5y=-2$
{$-3x-9y/2=0$
3rd.Adding the equation,
$(3x-3x)+(5y-9y/2)=-2+0$,
$0x+y/2=-2$
4th.
solving for $y$,
$y/2=-2$, $y=-4$
5th.Back-substituting into the original equation and solving for $x$,
$3x+5(-4)=-2$,
$3x-20=-2$,
$3x=18$,
$x=6$
6th. To check, we can substitute the answer into the roiginal equation and check for equal sign. If it's correct the answer is right, otherwise the answer is wrong and we need to redo our solution.
$2(6)+3(-4)=0$,
$12-12=0$,
$0=0$.
Therefore, the answer is right.
