Question

Which of the following systems of linear equations has an infinite number of solutions?

A. {
x=3
y=5
​


B. {
y=3x+3
3x−y=−3
​


C. {
3x−3=0
5y−5=0
​


D. None of the above

Answer 1

B.

Reason: In B, substituting y = 3x + 3 into 3x − y = −3 gives 3x − (3x + 3) = −3 → −3 = −3, an identity, so the second equation is dependent on the first and every point (x, 3x+3) is a solution (infinitely many). A and C each fix x and y uniquely.