How do you solve the system of equations $5x+2y=75, -x-2y=-31$ ?

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Answer 1 · 2016-12-10T14:12:49

$x = 11$ and $y = 10$

Step 1) Solve the second equation for $x$ :

$-x + x - 2y + 31 = -31 + 31 + x$

$-2y + 31 = x$

$x = -2y + 31$

Step 2) Substitute $-2y + 31$ into the first equation for $x$ and then solve for $y$ :

$5(-2y + 31) + 2y = 75$

$-10y + 155 + 2y = 75$

$8y + 155 = 75$

$8y + 155 - 155 = 75 - 155$

$8y = -80$

$(8y)/8 = 80/8$

$y = 10$

Step 3) Substitute $10$ for $y$ into the solution for the second equation and the end of Step 1).

$x = -2*10 + 31$

$x = -20 + 31$

$x = 11$

How do you solve the system of equations 5x+2y=75, -x-2y=-315x+2y=75, -x-2y=-31?