Digital SAT · Math · Algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A system of two linear equations asks for the pair (x, y) that makes both equations true at once. On a graph it is the point where the two lines cross.
Use substitution when one equation already gives x or y alone: put that expression into the other equation. Use elimination when both are in the form ax + by = c: multiply one or both equations so that one variable has matching coefficients, then add or subtract.
Two lines can also never meet or be the same line. Parallel lines give no solution. Identical lines give infinitely many solutions. Check this by comparing the ratios of the coefficients.
Stopping when the x and y coefficients are in the same ratio and calling it no solution. Compare the constants too: if they are in the same ratio as well, the lines are identical and there are infinitely many solutions.
Answer: (x, y) = (2, 5)
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