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.

Answer 1

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.