In math class, Emma and Angelle pair as a group. Emma’s task is to graph (7/2)x−(9/2)=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 (7/2)x−(9/2)=2y and 4y=7x−9 ?

Question

(1 point)
Responses

(1.286,0)
left parenthesis 1.286 comma 0 right parenthesis

(1.286,0) and (0,−2.25)
left parenthesis 1.286 comma 0 right parenthesis and left parenthesis 0 comma negative 2.25 right parenthesis

an infinite number of solutions
an infinite number of solutions

no solution
no solution
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Answer 1

To determine the solution of the equations \( (7/2)x - (9/2) = 2y \) and \( 4y = 7x - 9 \), we can start by rewriting both equations in a more comparable format.

1. Equation 1: \( (7/2)x - (9/2) = 2y \)

   • Rearranging this gives: \[ 2y = \frac{7}{2}x - \frac{9}{2} \]
   • Dividing everything by 2: \[ y = \frac{7}{4}x - \frac{9}{4} \]

2. Equation 2: \( 4y = 7x - 9 \)

   • Rearranging this to solve for y: \[ y = \frac{7}{4}x - \frac{9}{4} \]

Both equations are equivalent as they represent the same linear relationship.

Since both equations are the same line, they will intersect at an infinite number of points along the line. Thus, the system doesn't just have a unique solution; instead, every point on the line is a solution.

Therefore, the answer is:

an infinite number of solutions.