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?

Answer 1

To find the solution to the system of equations represented by the two equations, we can set them equal to each other:

(7/2) x - (9/2) = 2y and 4y = 7x - 9

Let's start by getting both equations in the form y = mx + b:

For the first equation, we can add (9/2) to both sides and then divide by 2:

(7/2) x - (9/2) + (9/2) = 2y + (9/2)
(7/2) x = 2y + (9/2)
(7/2) x / (7/2) = (2y + (9/2)) / (7/2)
x = (2y + (9/2)) * (2/7)
x = (4y + 9) / 7

For the second equation, we can divide by 4:

4y / 4 = (7x - 9) / 4
y = (7x - 9) / 4

Now we can set these two equations equal to each other:

(4y + 9) / 7 = (7x - 9) / 4

To get rid of the fractions, we can cross multiply:

4(4y + 9) = 7(7x - 9)
16y + 36 = 49x - 63

Now we can simplify and rearrange the equation:

16y = 49x - 63 - 36
16y = 49x - 99
16y - 49x = -99

So the solution to the system of equations is:

16y - 49x = -99