Systems of Linear Equations

SAT Math · Axiom Academy

Solving systems using substitution and elimination A system of linear equations is a set of two or more equations with two or more variables. The solution is the point(s) where all equations are satisfied simultaneously. We're looking for the values of x and y that make BOTH equations true. Use substitution when one equation is already solved for a variable. Example: Solve using substitution Use elimination when the equations are in standard form or when substitution is messy. Example: Solve using elimination How Many Solutions Can a System Have? During elimination, if you get a false statement like 0 = 5 , there's no solution. Substitution vs. Elimination: When to Use Each One variable is already isolated Coefficients are small and simple Substitution would create fractions Graphically: Systems questions might show you a graph. Look for the intersection point. Pick a method: If the system looks messy either way, try substitution first—it's less error-prone. Check your work: Substitute both values back into BOTH original equations. Watch for no solution/infinite: These appear on the SAT. Know the signs: 0 = 0 (infinite) vs. 0 = 5 (none).

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