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