# How do you solve this system of equations: 4x + 6y = - 78 and x - y = - 2?

May 3, 2018

$x = - 9$ and $y = - 7$

#### Explanation:

x−y=−2 ; 4x+6y=−78

Step 1: Solve x−y=−2 for $x$:

x−y (+y) =−2 (+y)
(Add $y$ to both sides)

x=y−2

Step 2: Substitute “y−2” for “$x$” in 4x+6y=−78 :

4x+6y=−78
4(y−2)+6y=−78
10y−8=−78
(Simplify both sides of the equation)

10y−8 (+8)=−78 (+8)
(Add $8$ to both sides)

10y=−70
10y/ (10)=−70/ (10)
(Divide both sides by $10$)

y=−7

Step 3: Substitute “−7” for “$y$” in x=y−2 :
(Simplify both sides of the equation)
x=y−2
x= (−7) −2

x=−9

$x = - 9$ and $y = - 7$