-4x-2y=-12
4x+8y=-24
Solve by elimination
And i need a solution
add the two equations to eliminate x
solve for y
substitute back to an original equation to find x
To solve the system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate the variable "x" by adding the two equations.
Given:
Equation 1: -4x - 2y = -12
Equation 2: 4x + 8y = -24
Add the two equations together:
(-4x - 2y) + (4x + 8y) = (-12) + (-24)
This simplifies to:
6y = -36
Divide both sides of the equation by 6 to isolate the variable "y":
6y/6 = -36/6
y = -6
Now, substitute the value of "y" back into one of the original equations (Equation 1):
-4x - 2(-6) = -12
Simplify:
-4x + 12 = -12
Subtract 12 from both sides:
-4x = -12 - 12
-4x = -24
Divide by -4 to solve for "x":
(-4x)/(-4) = (-24)/(-4)
x = 6
So, the solution to the system of equations is:
x = 6 and y = -6
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply the equations by appropriate numbers to make the coefficients of x or y terms in one equation equal in magnitude but opposite in sign to the corresponding terms in the other equation.
In this case, we can start by multiplying the first equation by 2 and the second equation by -1:
Equation 1: -8x - 4y = -24
Equation 2: -4x - 8y = 24
Step 2: Add the two equations together to eliminate one variable (either x or y).
(-8x - 4y) + (-4x - 8y) = (-24) + 24
-12x - 12y = 0
Simplifying the equation, we get:
-12(x + y) = 0
Step 3: Solve for the remaining variable.
We have -12(x + y) = 0, which means either x + y = 0 or -12 = 0.
If we set x + y = 0, then we can solve for y by substituting x = -y into either original equation:
-4(-y) - 2y = -12
4y - 2y = -12
2y = -12
y = -6
Now, substitute the value of y back into one of the original equations to solve for x:
-4x - 2(-6) = -12
-4x + 12 = -12
-4x = -24
x = 6
So the solution to the system of equations is x = 6 and y = -6.