Nonzero multiples of an equation remain equivalent. Match one variable’s coefficients, then subtract equal coefficients or add opposite coefficients. This eliminates that variable. Example Solve 2x+3y=12 and 3x-2y=5. Multiplying the first equation by 2 and the second by 3 gives 4x+6y=24 and 9x-6y=15. Adding gives 13x=39, so x=3. Substituting into 2x+3y=12 gives 6+3y=12, so y=2. Check: 3(3)-2(2)=5. Multiply every term, including the constant, when scaling an equation. When subtracting equations, subtract every term of the second equation.

Nonzero multiples of an equation remain equivalent. Match one variable’s coefficients, then subtract equal coefficients or add opposite coefficients. This eliminates that variable.

Solve \(2x+3y=12\) and \(3x-2y=5\). Multiplying the first equation by \(2\) and the second by \(3\) gives \(4x+6y=24\) and \(9x-6y=15\).

Adding gives \(13x=39\), so \(x=3\). Substituting into \(2x+3y=12\) gives \(6+3y=12\), so \(y=2\).

Check: \(3(3)-2(2)=5\). Multiply every term, including the constant, when scaling an equation. When subtracting equations, subtract every term of the second equation.

Elimination by matching coefficients

Elimination by matching coefficients