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. The both get exactly the same graph. What is the solution of (7/2) x - (9/2) = 2y and 4y = 7x - 9?
A. (1.286,0)
B. an infinite number of solutions
C. no solution
D. (1.286,0) and (0, -2.25)
To find the solution for the given equations, let's first solve each equation separately.
1. (7/2)x - (9/2) = 2y:
To put the equation in slope-intercept form (y = mx + b), we need to isolate y.
(7/2)x - (9/2) = 2y
(7/2)x - (9/2) + (9/2) = 2y + (9/2)
(7/2)x = 2y + (9/2)
2y = (7/2)x - (9/2)
y = (7/4)x - (9/4)
2. 4y = 7x - 9
To put this equation in slope-intercept form, we need to isolate y.
4y = 7x - 9
(1/4)(4y) = (1/4)(7x - 9)
y = (7/4)x - 9/4
Comparing the equations, we can see that they are indeed the same:
y = (7/4)x - (9/4)
This means that the two equations represent the same line, and they intersect at every point on that line. Hence, the solution to the system of equations is an infinite number of solutions.
Therefore, the correct answer is B. an infinite number of solutions.