Verified Answer :

Take one equation away from the other. This cancels out the -5x, so you can work out y.

-5x+7y=11 -
-5x+3y=19
---------------
4y=-8
y=-2

Then add the y into one of the equations, and solve.

-5x-6=19
-5x=25
x=-5

To check, add both x and y into the other equation.

25-14=11

That is correct, so we know that our working is correct.

x=-5
y=-2

:)

\(\left\{\begin{array}{ccc}-5x+7y=11\\-5x+3y=19&/\cdot(-1)\end{array}\right\\+\left\{\begin{array}{ccc}-5x+7y=11\\5x-3y=-19\end{array}\right\\-------------\\.\ \ \ \ \ \ \ \ 4y=-8\ \ \ \ |divide\ both\ sides\ by\ 4\\.\ \ \ \ \ \ \ \ \ y=-2\\5x-3(-2)=-19\\5x+6=-19\\5x=-19-6\\5x=-25\ \ \ \ \ |divide\ both\ sides\ by\ 5\\x=-5\\\\Answer:x=-5\ and\ y=-2\)

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