Solving 3x + 2y = 12 and 5x - 2y = 4

Algebra 1 · Axiom Academy

EXAMPLE Solving 3x + 2y = 12 and 5x − 2y = 4 Direct elimination when the coefficients are already opposites: add the equations so one variable cancels. Solve the system of equations using the elimination method. Elimination Method: Key Takeaways Nice work — you solved the system by elimination. Here is a recap of the process: Identify opposites: we looked for a variable whose coefficients were opposites ( +2y and -2y ). This is the easiest case for elimination. Eliminate by adding: we added the two equations, causing the y terms to cancel and leaving a single equation in x . Solve for one variable: we solved 8x = 16 to get x = 2 . Back-substitute: we put x = 2 into an original equation to find y . State the solution: the answer is the ordered pair (2, 3) , where the two lines intersect. When a variable's coefficients are already opposites, adding the equations is the fastest route — no multiplying needed first.

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