Substitution Method Preview

Pre-Algebra · Axiom Academy

LESSON The Substitution Method Graphing two lines only points at where they cross. Substitution turns the system into one equation and lands the exact answer. 1. Graphing Points At the Answer Take a system of two lines. Graph both, and their crossing point is the one (x, y) that satisfies both equations at once: 2. Substitute an Equal Expression Line 1 already tells us what y equals: y = 2x - 2 . The whole idea of substitution is that wherever an equation contains y , we may drop in 2x - 2 in its place — because they are the same number. Line 1 is already isolated: y = 2x - 2 . One variable is written in terms of the other. Line 2 is x + y = 7 . Replace its y with 2x - 2 . The result, x + (2x - 2) = 7 , has only x in it — no y left to chase. A single-variable linear equation is something you already know how to solve. 3. Solve It, and the Exact Point Appears With one variable, the rest is routine. Solve for x , then put that value back into Line 1 to get y — and the answer the graph could only gesture at snaps into place exactly. Combine like terms: x + (2x - 2) = 7 becomes 3x - 2 = 7 . Solve for x : add 2 to get 3x = 9 , then divide to get x = 3 . Back-substitute into Line 1: y = 2(3) - 2 = 4 . The solution is the exact point (3, 4) — and it sits right where both lines cross. "Somewhere up and to the left of center" — a region, not a point. x = 3 , y = 4 — the precise coordinates, with no reading off a grid.

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