Question

Which equation, when paired with the equation 2y – 4x = 12, will result in a system having infinitely many solutions?

a) –y – 2x = 6
b) –y + 2x = 12
c) y = 2x + 6
d) y = 2x + 12

Answer 1

To create a system of equations with infinitely many solutions, the ratio of the coefficients of x and y should be the same in both equations.

Step-by-step explanation:

To create a system of equations with infinitely many solutions, we need the equations to be equivalent. This means that the ratio of the coefficients of x and y should be the same in both equations. Let's check each option:

• Option a) -y - 2x = 6: The ratio of the coefficients is -1/-2 = 1/2.
• Option b) -y + 2x = 12: The ratio of the coefficients is -1/2 = -1/2.
• Option c) y = 2x + 6: The ratio of the coefficients is 1/2.
• Option d) y = 2x + 12: The ratio of the coefficients is 1/2.

Since options c) and d) have the same ratio as the given equation 2y - 4x = 12, both of them will result in a system having infinitely many solutions.