SAT Math: No Solution or Infinitely Many Solutions
28+ practice questions in Praczo
The concept, explained
- 1
A linear equation has no solution when simplification produces a false statement like 3 = 7. No value of x can satisfy it.
- 2
A linear equation has infinitely many solutions when simplification produces a true statement like 0 = 0. Every value of x works.
- 3
For a system of two linear equations: parallel lines (same slope, different y-intercepts) → no solution. Identical lines (same slope, same intercept) → infinitely many solutions.
- 4
The SAT often asks: "For what value of k does this equation have no solution?" Set up the equation so the variable cancels and the remaining constants are unequal.
- 5
For no solution: equal coefficients on x, unequal constants. For infinite solutions: equal coefficients on x, equal constants.
- ✗ Confusing no solution with x = 0. Getting x = 0 is still a solution. "No solution" means the variable disappears entirely and leaves a false statement.
- ✗ For systems, checking only the slopes without also checking the intercepts when identifying infinite solutions.
SAT-style practice
The equation 4x + 8 = 4x + k has no solution. What must be true of k?
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required