Substitution
Use one equation to replace a variable in the other, solve the resulting one-variable equation, then back-substitute and check the ordered pair.
Solve the system of equations below by substitution. Show all algebraic steps. State the solution as an ordered pair, then check it in both original equations.
One ordered pair (x, y) that makes both equations true at the same time.
Use the equation that already tells you what a variable equals.
Equation 1 already says y = x + 1. Equal quantities can replace one another, so the y in Equation 2 can become x + 1 without changing the solution.
Click x + 1, then click the y in Equation 2.
The replacement works because Equation 1 tells us that y and x + 1 have the same value for every solution of that equation.
Replacing one with the other is called substitution. The substitution itself is only the first move. Its purpose is to turn a two-variable system into an ordinary one-variable equation that you can solve with equality-preserving moves.
Choose the easy equation
Look for a variable that is already isolated, or isolate one first.
Substitute
Equal quantities may replace one another. Use parentheses to keep a multi-term expression together.
Solve
Simplify expressions, then undo operations with equal moves on both sides.
Back-substitute + check
Find the second coordinate, then verify the ordered pair in both originals.
Substitute the whole expression.
If x = y + 4, then 2x + y becomes 2(y + 4) + y. The parentheses matter because the coefficient 2 multiplies the entire replacement.
Solve a new system without answer choices.
Solve the system by substitution. Show each algebraic step and check your ordered pair.
Now try a few without the walkthrough.
Solve each system by substitution on paper or in your notebook. Show the substitution, solve, back-substitute, and check.