AlgebraMedium
Systems of two linear equations in two variables
Solve systems of linear equations using substitution and elimination, and interpret the number of solutions.
Sample SAT Problem
Solve: 2x + y = 10 and x − y = 2.
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Step-by-Step Solution
Add the equations: 3x = 12, x = 4. Substitute: y = 2. Solution: (4, 2).
Key Tips from Pamela
- If the lines are parallel (same slope, different intercept), there is no solution.
- If they are the same line, there are infinitely many solutions.
- Elimination is fastest when coefficients are easy to match.
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