In math class, Emma and Angelle pair as a group. Emma’s task is to graph (72)x−(92)=2y and Angelle’s task is to graph 4y=7x−9 . After they complete their graphs, they compare their work. They both get exactly the same graph. What is the solution of (72)x−(92)=2y and 4y=7x−9 ? Responses

Question

no solution
(1.286,0) and (0,−2.25)
(1.286,0)
an infinite number of solutions

Answer 1

The correct response is an infinite number of solutions.

To determine this, we can simplify both equations and see that they are equivalent.

First, let's simplify the equation (72)x - (92) = 2y:
(72)x - (92) = 2y
72x - 92 = 2y
36x - 46 = y

Now, let's simplify the equation 4y = 7x - 9:
4y = 7x - 9
y = (7x - 9)/4

We see that y is equal to (7x - 9)/4, which is the same as y = 36x - 46.

This means that both equations represent the same line when graphed, and therefore they have an infinite number of solutions.