Simultaneous Equations

Section 1What the solution means

For two linear equations in x and y, the solution is an ordered pair (x, y) that makes both equations true. On a graph, it is the point where the two lines meet.

Section 2Elimination method

Elimination works by adding or subtracting equations to remove one variable. If the x or y coefficients already match, eliminate that variable first.

Section 3Making coefficients match

Sometimes you must multiply one or both equations before eliminating. For example, if one equation has 2x and the other has 3x, multiply to make both coefficients 6x.

Section 4Substitution method

Substitution works by making one variable the subject, then replacing it in the other equation. It is useful when one equation already says something like y = 2x + 1.

Section 5Checking your answer

Always substitute your x and y values into both original equations. If both equations are true, the solution is correct.