ACT Preparation / Unit 9 ACT 0829 worked example, 60 to 90 seconds
Solving a System by Elimination
The idea
Elimination runs in four steps. First, line up both equations in the form ax + by = c. Second, choose a variable and multiply one or both equations so its coefficients are opposites. Third, add the equations, which removes that variable, and solve for the other. Fourth, substitute back into either original equation for the second variable, and check both.
In practice
Worked example: 3x + 4y = 10 and 2x − 3y = 1. Step two: to eliminate x, multiply the first by 2 and the second by −3, giving 6x + 8y = 20 and −6x + 9y = −3. Step three: 17y = 17, so y = 1. Step four: 3x + 4 = 10, so x = 2. Check: 4 − 3 = 1.
Where people slip
Choose the variable that needs the smaller multipliers. Eliminating y here would need multipliers of 3 and 4, with larger numbers to carry.
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