SAT Systems of Linear Equations study notes

A solution to a system makes both equations true at once. Elimination is often fastest when one pair of coefficients already matches; subtraction then removes that variable. If the variable terms cancel and leave a false statement, the lines are parallel. If everything cancels to a true statement, they are the same line.

Worked example

Adult tickets cost a and student tickets cost s. If 2a + 3s = 55 and 4a + s = 65, find a − s.

From the second equation, s = 65 − 4a. Substituting into the first gives 2a + 195 − 12a = 55, so a = 14. Then s = 9 and a − s = 5.

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