Do you need to add or subtract the equations $5x+7y=-31$ and $5x-9y=17$ to solve the system?

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Answer 1 · 2018-05-19T20:22:57

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Given: $5x + 7y = -31; " and " 5x -9y = 17$

Since both equations have a $5x$ , subtract one from the other to eliminate the $x$ terms:

$" "5x + 7y = -31$
$ul(-(5x -9y = " "17" "))$
$" " 16y = -48; " "y = -48/16 = -3$

Substitute this value for $y$ in either of the equations to find the value of $x$ :

$5x +7(-3) = -31$

$5x -21 = -31$

Add $21$ to both sides: $" "5x = -31 + 21 = -10$

$x = -10/5 = -2$

Check your answer by substituting both $x$ and $y$ into the other equation:

$5(-2) - 9(-3) = 17$

$-10 +27 = 17$ , which is TRUE

Solution: is a point (-2, -3)
which is the intersection point common to both lines

Do you need to add or subtract the equations 5x+7y=-315x+7y=-31 and 5x-9y=175x-9y=17 to solve the system?