solve using the elimination method. -2x-8y=-42
-4x+6y=-18
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant(s) in order to create a common coefficient for one of the variables.
Looking at the given system:
-2x - 8y = -42 ...........(Equation 1)
-4x + 6y = -18 ...........(Equation 2)
If we multiply Equation 1 by -2, it will result in a -4x term that can be eliminated when added to Equation 2.
-2 * (-2x - 8y) = -2 * (-42)
4x + 16y = 84 ...........(Equation 3)
The equations become:
4x + 16y = 84 ...........(Equation 3)
-4x + 6y = -18 ...........(Equation 2)
Step 2: Add the modified equations together to eliminate one variable.
Adding Equation 2 and Equation 3:
(4x + 16y) + (-4x + 6y) = 84 + (-18)
4x - 4x + 16y + 6y = 66
22y = 66
Simplifying the equation:
22y = 66
Divide both sides of the equation by 22 to isolate y:
22y/22 = 66/22
y = 3
Step 3: Substitute the value of y back into one of the original equations to solve for x.
Let's use Equation 1:
-2x - 8(3) = -42
-2x - 24 = -42
Subtract -24 from both sides:
-2x = -42 + 24
-2x = -18
Divide both sides of the equation by -2 to isolate x:
-2x / -2 = -18 / -2
x = 9
Therefore, the solution to the system of equations is x = 9 and y = 3.