Elimination
Add or scale whole equations so one variable becomes an additive inverse pair and disappears, leaving a simpler equation with the same shared solution.
Solve the system of equations by elimination. Show your algebraic steps. State the solution as an ordered pair, then check it in both original equations.
One equation contains +y; the other contains −y. What happens to that pair if the two true equations are added column by column?
Let the opposite terms erase each other.
Add Equation 1 and Equation 2
Add left side to left side and right side to right side. If A = B and C = D, then A + C = B + D.
Elimination works because we combine entire equalities. At the system’s shared solution, both original equations are true. Adding two true equalities creates another true equality.
We arrange the equations so one variable appears as additive inverses, such as +y and −y. Their sum is zero, so that coordinate disappears from the new equation. The cancellation is ordinary arithmetic, not a special algebra trick.
Align like terms
Treat each equation as one complete equality.
Create opposites if needed
Scaling an entire equation by the same nonzero factor preserves its solutions.
Combine the equations
Choose addition or subtraction so one variable has coefficient 0.
Recover + verify
The final ordered pair must satisfy both original equations.
Scale the whole equation, not the convenient term.
If you multiply an equation by −2, that factor must reach every term on the left and the right. Changing only one coefficient creates a different equation and can destroy the original solution set.
This time the coefficients are not opposites yet.
Solve the system by elimination. First create opposite x-coefficients, then combine the equations.
Choose a legal move that will eliminate x.
Equation 2 already has +2x. Create −2x in the other row without changing its solutions.
Now choose the cancellation strategy yourself.
Solve each system by elimination. Show any equation scaling, combine the rows, back-substitute, and check the ordered pair.