Question

Mr. Brown is creating examples of systems of equations. He wants to have a system of equations with infinite solutions that includes the equation 5x + 2y = 8. Which equation could Mr. Brown use to complete the system so that it has infinite solutions?
2x + 5y = 8
15x + 6y = 21
1.25x +0.5y = 2
6.5x + 3.5y = 9.5

Answer 1

The equation that Mr. Brown could use to complete the system is 1.25x + 0.5y = 2 so that it has infinite solutions.

Answer 2

Answer: The answer is (C) 1.25x + 0.5y =2.

Step-by-step explanation: One equation from the system of equations is given by

5x + 2y = 8.

We are to select the second equation such that the system will have an infinite number of solutions.

In such a case, we must have that the corresponding coefficients of 'x', 'y' and the constant term must be proportional.

We can see that for the equation 1.25x + 0.5y = 8,

$\dfrac{5}{1.25}=\dfrac{2}{0.5}=\dfrac{8}{2}=4.$

Thus, (C) is the correct option.