SAT Math: Infinite Solutions in Linear Systems
33+ practice questions in Praczo
The concept, explained
- 1
A system of two linear equations has infinitely many solutions if they represent the EXACT SAME line.
- 2
This means their slopes AND y-intercepts must be identical.
- 3
If given equations in the form ax + by = c and dx + ey = f, they have infinite solutions if the ratio of their coefficients aligns: a/d = b/e = c/f.
- 4
Sometimes the SAT presents a single equation with variables on both sides; it has infinite solutions if it simplifies to a true statement like 5 = 5 or 2x = 2x.
- 5
If it simplifies to a false statement (e.g., 5 = 3), there is NO solution.
- ✗ Confusing "infinite solutions" with "no solution" (no solution means same slope but DIFFERENT y-intercepts).
- ✗ Forgetting to distribute a negative sign before determining if the two sides of an equation are identical.
SAT-style practice
If the system of equations 2x + 3y = 7 and 4x + cy = 14 has infinitely many solutions, what is the value of c?
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