➕ Algebra 1 · Systems of Equations
Solving Systems by Graphing cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The method (GRID)
- G: Get each equation ready, y = mx + b
- R: Ruler-draw both lines on one grid
- I: Identify the crossing, (x, y)
- D: Double-check in both equations
Three outcomes (non-vertical lines)
- Different slopes: one solution
- Same slope, different b: no solution (parallel)
- Same slope, same b: infinitely many solutions (same line)
Exact or estimate?
- Clean grid point and the check works: exact
- Between grid lines: an estimate, so check it and use algebra
Example
- y = x + 2 and y = −3x + 6
- They cross at (1, 3)
- Check: 3 = 1 + 2 and 3 = −3(1) + 6
Watch out
- Check in both equations
- A solution is a pair (x, y)
- Same slope: compare b
Formulas
- Solution of a system: An ordered pair (x, y) that makes both equations true
- One solution: m1 ≠ m2 (non-vertical lines with different slopes): the lines cross exactly once
- No solution: m1 = m2 and b1 ≠ b2: parallel lines
- Infinitely many solutions: m1 = m2 and b1 = b2: the same line
- x-coordinate of the crossing: Solve m1x + b1 = m2x + b2 for x, then find y
Solving Systems by Graphing cheat sheet from HighSchoolQ.com, for personal study use.