A solution to a system must satisfy every equation at the same time. Use substitution, elimination or a graph depending on which method exposes the unknown efficiently.
Key Rules
Substitute when one equation already isolates a variable.
Add or subtract equations when coefficients cancel.
For two linear equations, intersecting lines have one solution; distinct parallel lines have none; the same line has infinitely many.
Common Mistakes to Avoid
Checking a result in only one of the equations.
Losing a negative sign when subtracting an entire equation.
SAT Strategy Tips
→If the question asks for a combination such as x + y, look for a direct route to that combination.
→Use graphing to confirm an intersection, but interpret the coordinates correctly.
Example Question
If x + y = 12 and x − y = 4, what is x?
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