The solution for the system of equations is (2,-4).
The given system of equations are x + 2y = -6-----(1) and 6x + 2y = 4-----(2).
How do solve systems of equations using the substitution method?
To solve a system of equations using substitution:
- Step 1: Isolate one of the two variables in one of the equations.
- Step 2: Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. This should result in a linear equation with only one variable.
- Step 3: Solve the linear equation for the remaining variable.
- Step 4: Use the solution of Step 3 to calculate the value of the other variable in the system by using one of the original equations.
Now, rearrange x+2y=-6 to solve for x:
So, x = -2y-6
Substitute -2y-6 for x into the second equation 6x + 2y = 4.
That is, 6(-2y-6) + 2y = 4
⇒-12y-36 + 2y = 4
⇒-10y = 40
⇒y = -4
By substituting y = -4 in x = -2y-6 we get x=2.
Therefore, the solution for the system of equations is (2,-4).
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