To use the elimination method with multiplication for this system of equations, we need to manipulate the equations so that the coefficients of either the x or y terms will be the same or opposites.
First, let's multiply the second equation by 2 to make the coefficients of x the same.
2 * (- 2x + 4y) = 2 * 30
Simplifying this, we get -4x + 8y = 60.
Now we have the two equations:
4x - 6y = - 48 (Equation 1)
- 4x + 8y = 60 (Equation 2)
By adding the two equations vertically, we can eliminate the x variable:
(4x - 6y) + (-4x + 8y) = (-48) + 60
Simplifying this equation, we get:
-6y + 8y = 12
2y = 12
Dividing both sides by 2, we find:
y = 6
Now, we substitute this value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
4x - 6(6) = - 48
Simplifying this equation, we get:
4x - 36 = -48
To isolate the x variable, we add 36 to both sides:
4x = -12
Dividing both sides by 4, we find:
x = -3
So the solution to the system of equations is x = -3 and y = 6.
Solve the system of two equations using elimination with multiplication.
4x - 6y = - 48
- 2x + 4y = 30 (1 point)
1 answer