Question 459179
I always appreciate when a student tells us what they've tried so far. Good work! 
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I see a small arithmetic error in your first equation. Multiplying the right side by 2 gives (2)(-20)=-40 so your new equation would be -14x+10x=-40.
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Add the two equations,
{{{-14x+10y=-40}}}
{{{-15x-10y= 40}}}
to give,
{{{-29x=0}}}
Divide both sides by -29.
{{{x=0}}}
Now, substitute 0 for x into one of the original equations to find the y-value. It doesn't matter which one.
{{{-7x+5y=-20}}}
{{{-7(0)+5y=-20}}}
{{{5y=-20}}}
{{{y=-4}}}
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So, the solution to your system of equations is the order pair (0,-4). It's always a good idea to check your work for possible errors.
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CHECK:
{{{-7x+5y=-20}}}
{{{-7(0)+5(-4)=-20}}}
{{{0-20=20}}}
{{{-20=-20}}} 
Good. Now check the other equation.
{{{-3x-2y=8}}}
{{{-(0)-2(-4)=8}}}
{{{8=8}}}

Winner, winner, chicken dinner! (o: