Solving x + y = 7 and 2x - y = 2

Algebra 1 · Axiom Academy

EXAMPLE Solving x+y=7 and 2x−y=2 Solving a system of two linear equations using the substitution method. Solve the system x + y = 7 and 2x - y = 2 by substitution. Find the ordered pair (x, y) that satisfies both equations at once. Key Takeaways: The Substitution Method Nice work — you solved a system of equations by substitution. Here's the process to carry forward: Isolate: Solve one equation for one variable (here, y = 7 - x from the simpler equation). Substitute: Plug that expression into the other equation, never the one you started from. Solve: Distribute carefully, combine like terms, and solve the resulting one-variable equation. Back-substitute: Use that value in the isolated form to get the second variable. Result: The system x + y = 7 and 2x - y = 2 has the unique solution (3, 4) . Substitution turns a two-variable system into a single equation you already know how to solve — and the check confirms the lines truly cross at that point.

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