Solve the system of equations using elimination: minus, x, minus, 3, y, equals, minus, 7−x−3y=−7 and minus, 5, x, minus, 3, y, equals, 25−5x−3y=25.

1 answer

To solve this system of equations using elimination, we will eliminate one variable by adding the equations together or subtracting one from the other.

First, let's write the system of equations:

Equation 1: -x - 3y = -7
Equation 2: -5x - 3y = 25

Let's eliminate the y variable by adding the two equations together:

(-x - 3y) + (-5x - 3y) = (-7) + (25)

Combining like terms, we get:

-6x - 6y = 18

Dividing both sides of the equation by -6, we get:

x + y = -3 Equation 3

Now let's eliminate the x variable by subtracting Equation 1 from Equation 2:

(-5x - 3y) - (-x - 3y) = 25 - (-7)

Simplifying, we get:

-4x = 32

Dividing both sides of the equation by -4, we get:

x = -8

Now substitute the value of x into Equation 3:

(-8) + y = -3

Simplifying, we get:

y = 5

Therefore, the solution to the system of equations is x = -8 and y = 5.