SAT and ACT math terms · SAT Math, ACT Math
System of linear equations
System of linear equations: Two or more linear equations with the same variables, solved together to find values that satisfy all of them.
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What it means
A system of two linear equations can have one solution (lines intersect), no solution (parallel lines with different intercepts) or infinitely many solutions (the same line). Common solving methods are substitution, elimination and graphing.
A system has no solution when the equations have the same slope but different intercepts, and infinitely many when one equation is a multiple of the other.
Example
x + y = 10 and x − y = 4. Adding gives 2x = 14, so x = 7 and y = 3.
On the exam
Both tests ask you to solve systems, set up systems from word problems, and determine for which constant a system has no or infinitely many solutions.