SATAdvanced (700+)Frequency: 2 questions
Linear Systems: No Solution & Infinite Solutions
Two linear equations have: NO SOLUTION if lines are parallel (same slopes, different y-intercepts); INFINITELY MANY SOLUTIONS if equations represent the exact same line (same slope, same y-intercept); EXACTLY ONE SOLUTION if slopes are different.
Core Formula & Concept Cheat Sheet
1No solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
2Infinitely many solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
3Standard form: Ax + By = C has slope m = -A/B
Desmos Speed-Run Trick
Graph both equations with a slider for the unknown constant k. Observe when the lines become parallel or overlap.
The 700+ Score Trap
Setting constants equal without aligning the coefficients of x and y first.
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
In the system of equations:
3x - 2y = 12
9x - ky = 40
For what value of constant k does the system have no solution?
Frequently Asked Questions
What does no solution mean graphically?
It means the two lines are parallel and never intersect.