Steps for Solving by Substitution

Property 1. Rearrange one equation to be in the form $y = mx + b$ or $x = my + b$. 2. Substitute this expression into the other equation. 3. Solve the new equation for the single variable. 4. Substitute this value back into one of the original equations to find the second variable. 5. Write the solution as an ordered pair $(x, y)$. Explanation Think of it as a secret agent mission! You find a secret identity for one variable, like $y = 2x 5$, and then substitute this disguise into the other equation to unmask the first value. With that clue, you can plug it back into any original equation to find the partner variable. Mission accomplished, case closed! Examples For the system $y = 2x + 1$ and $y = x + 10$, substitute to get $2x + 1 = x + 10$. Solving $2x + 1 = x + 10$ gives $3x = 9$, so $x = 3$. Then, find y: $y = 2(3) + 1 = 7$. The solution is $(3, 7)$. For $x = 4y 2$ and $2x + y = 10$, substitute for $x$ to get the new equation: $2(4y 2) + y = 10$.