Question

A system of equations has infinitely many solutions. If 2y – 4x = 6 is one of the equations, which could be the other equation?

A. y = 2x + 6
B. y = 4x + 6
C. –y = –2x – 3
D. –y = –4x + 6

Answer 1

C

Explanation:

When a system of equations has an infinite number of solutions, this means that the equations will be identical.

Convert the given equation to y = mx + b form.

2y - 4x = 6

2y = 4x + 6

y = 2x + 3

Answer A, B, and D don't apply.

Answer C is the answer because if it is the same equation but with a negative sign in front of each term. If you switch the signs on every single term, you will have the given equation.

Answer 2

C

Explanation:

A system of equations has infinitely many solutions when the two lines representing the equations coincide. i.e. the two equations are the same or a multiple of each other.

2y - 4x = 6

2y = 4x + 6

2y = 2(2x + 3)

y = 2x + 3

-y = -(2x + 3)

-y = -2x - 3

Hence the other equation is -y = -2x - 3