The steps for solving a system of equations using elimination are:
1. Find the variable with equal or opposite coefficients.
2. If equal, subtract equations. If opposite, add the equations.
3. Solve the resulting one-variable equation.
4. Substitute the known value into the other equation and solve for the remaining variable.
Let's attempt solving a system using these steps.
2x + 4y = 8
-2x + 6y = 2
First step: Find the variable with equal or opposite coefficients.
The variable terms with equal or opposite coefficients are the x-terms - they are 2x and -2x (opposite terms).
Second step: If equal, subtract equations. If opposite, add the equations.
The coefficients are opposite, thus we must add the equations.
2x + 4y = 8
-2x + 6y = 2
+____________
0 + 10y = 10
Third step: Solve the resulting one-variable equation.
0 + 10y = 10
10y = 10
y = 1
Fourth step: Substitute the known value into the other equation and solve for the remaining variable.
-2x + 6y = 2
-2x + 6(1) = 2
-2x + 6 = 2
-2x = -4
x = 2
The solution to this system is (2, 1).