Solve the system of equations using elimination: 5, x, plus, 8, y, equals, minus, 885x+8y=−88 and x, minus, y, equals, minus, 2x−y=−2.
To solve the system of equations using the elimination method, we need to eliminate one variable by performing operations on the two equations.
Let's start with the first equation:
5x + 8y = -88
We can then multiply the second equation by 8 to match the coefficient of y in the first equation and obtain:
8x - 8y = -16
Now, let's add the two equations together:
5x + 8y + 8x - 8y = -88 - 16
This simplifies to:
13x = -104
Divide both sides by 13 to solve for x:
x = -104/13
x = -8
Now substitute this value of x into one of the given equations, let's use the second equation:
-2x - y = -2
Replace x with -8:
-2(-8) - y = -2
16 - y = -2
Now, isolate y:
-y = -2 - 16
-y = -18
y = 18
Therefore, the solution to the system of equations is x = -8 and y = 18.