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

May 19, 2018

#### Explanation:

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

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

$\text{ } 5 x + 7 y = - 31$
$\underline{- \left(5 x - 9 y = \text{ "17" }\right)}$
$\text{ " 16y = -48; " } y = - \frac{48}{16} = - 3$

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

$5 x + 7 \left(- 3\right) = - 31$

$5 x - 21 = - 31$

Add $21$ to both sides: $\text{ } 5 x = - 31 + 21 = - 10$

$x = - \frac{10}{5} = - 2$

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

$5 \left(- 2\right) - 9 \left(- 3\right) = 17$

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

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