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

In order to have a system of equations with infinite solutions, the equations must be equivalent. Two equations can be tested if they are equivalent by manipulating the equations such that they have equal coefficients for x or y.

We can take the coefficient of x as an example.

First, we reduce the coefficient of x of the given equation to 1 to make it simpler. We divide the whole equation by 5 and we get:

x + (2/5) y = 8/5

We do the same to the given options of equations.

We divide equation 1 with 2, equation 2 with 15, equation 3 with 1.25 and equation 4 with 6.5.

Compare the result with the given equation divided by 5 or x + (2/5) y = 8/5 and if it is the same, then the two equation are equivalent.

The third option: 1.25x + 0.5y = 2 will give you the same equation.