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.
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.