No Solution or Infinitely Many Solutions
Practice recognizing special solution cases in linear equations by comparing coefficients and constants.
Keyboard Shortcuts
💡 Pro tip: Use keyboard shortcuts for faster studying!
Study Smart Tips for No Solution or Infinitely Many Solutions
Master these concepts using proven study techniques that actually work:
Active Recall
Test yourself before flipping each card to strengthen memory retention
Spaced Repetition
Review difficult cards more frequently than easy ones
Multiple Sessions
Break study time into shorter, focused sessions
Explain Aloud
Verbalize answers to reinforce understanding
Questions Covered in This Set
10 cards to master
What are the three possible endings when simplifying a linear equation?
x = a number (one solution), a true statement like 8 = 8 (infinitely many), or a false statement like 8 = 5 (no solution).
Coefficients differ on each side → how many solutions?
Exactly one solution.
Coefficients match but constants differ → how many solutions?
No solution (the lines are parallel).
Coefficients match AND constants match → how many solutions?
Infinitely many solutions (an identity — the same line).
In cx + 12 = 5x + 12, what value of c gives infinitely many solutions?
c = 5. The constants already match, so the coefficients must match too.
ax − 7 = 3x + 2 has no solution for what value of a?
a = 3. Constants already differ (−7 vs 2), so matching coefficients forces no solution.
6(2x + 5) = kx + 30 has infinitely many solutions. Find k.
Distribute: 12x + 30 = kx + 30, so k = 12.
How many solutions does 5x − 3 = 5x + 3 have?
None. Coefficients match but constants don't, so it reduces to −3 = 3, which is false.
Find b so that −2(x − 3) = bx + 6 has infinitely many solutions.
Left side is −2x + 6, so b = −2.
What's the test-day shortcut for these questions?
Don't solve for x. Distribute, write each side as #x + #, then just match the numbers.
