Hey there!
y = -2x - 9
6x - 5y = -19
We're going to label the first equation as "1" and the second equation as "2." Now, in order to find the values of "x" & "y," we need to even out the equations by placing their "x" and "y" markers on the same side of the equal sign.
Let's start off by adding 2x to both sides of equation 1.
1) y + 2x = -2x - 9 + 2x
Simplify.
Equation 1 is now: 2x + y = -9
Now, we need to multiply equation 1 equations by "3" in order to create "6x" in both equations. This helps us find the value of "y" because it cancels out the "x" in both equations.
1) (2x + y = -9) × 3
Simplify.
1) 6x + 3y = -27
2) 6x - 5y = -19
Now that our equations are lined up, we can subtract equation 2 from equation 1.
- 6x - 6x = 0
- 3y - (-5y) = 3y + 5y = 8y
- -27 -(-19) = -27 + 19 = -8
Let's put this all together now.
8y = -8
Divide both sides by 8!
8y ÷ 8 = -8 ÷ 8
Simplify.
<h2>
y = -1</h2>
Now that we have the value of y, we can easily plug it into one of our equations to get our "x" value.
Equation 1: y = -2x - 9
Plug in "-1" for "y."
-1 = -2x - 9
Add 9 to both sides
-1 + 9 = -2x - 9 + 9
Simplify.
8 = -2x
Divide both sides by -2.
8 ÷ -2 = -2x ÷ -2
Simplify.
<h2>-4 = x</h2>
Therefore, x = -4 & y = -1
<h2>
(-4, -1) </h2>
Hope this helped! :)
