If the system of equations { 2x + 3y = 10, 4x + 6y = c } has infinitely many solutions, find c.
A10
B15
C20
D25
Answer & Solution
Correct answer: C. 20
Infinitely many solutions means one equation is a scalar multiple of the other. Multiply first by 2: 4x + 6y = 20. So c = 20. (Alternative: dividing 4x + 6y by 2 must give 2x + 3y = 10, so c/2 = 10, c = 20.)
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