SAT Math · Study & Practice
Systems of Linear Equations
A system of linear equations asks for values that satisfy two equations at once — a frequent and high-value SAT topic. This chapter covers the graphical, substitution and elimination methods, plus translating word problems into systems. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Graphical Method
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2
Substitution Method
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3
Elimination Method
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4
Word Problems
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Chapter test
Formula Reference Sheet
This chapter
Methods
| Graphical | solution = intersection point of the two lines |
|---|---|
| Substitution | solve one equation for a variable, plug into the other |
| Elimination | add/subtract equations to cancel a variable |
Number of solutions
| One solution | lines cross (different slopes) |
|---|---|
| No solution | parallel lines (same slope, different intercept) |
| Infinite solutions | same line (identical equations) |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
🖩 Graphing Calculator