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?
1. an infinite number of solutions
2. (1.286,0) and (0,-2.25)
3. (1.286,0)
4. no solution
To find the solution to the system of equations (7/2)x - (9/2) = 2y and 4y = 7x - 9, we can simplify both equations and compare them.
For the first equation, we can move the 2y term to the other side and write it as:
(7/2)x - 2y = 9/2.
Now, let's multiply both sides of the equation by 2 to eliminate the fraction:
2 * (7/2)x - 2 * 2y = 2 * (9/2),
7x - 4y = 9.
We now have the equation 7x - 4y = 9.
If we compare this equation to the second equation 4y = 7x - 9, we notice that they are identical. This means that the two equations represent the same line.
When two equations represent the same line, the system has an infinite number of solutions. This is because any point on the line will satisfy both equations.
Therefore, the solution to the system of equations is 1. an infinite number of solutions.