Question

Use the image to answer the question.

One line, graphed as both solid and a dotted, is graphed on a coordinate plane. The x-axis ranges from negative 10 to 10 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
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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
?

(1 point)

an infinite number of solutions

(1.286,0)


no solution

(1.286,0)
and (0,−2.25)

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Answer 1

Infinite number of solutions.

Reason: (7/2)x − (9/2) = 2y implies y = (7/4)x − 9/4, and 4y = 7x − 9 also gives y = (7/4)x − 9/4. The equations are the same line, so they share all points.