Question

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
?

Answer 1

Both equations are the same line. Solve either for y:

(7/2)x − (9/2) = 2y => y = (7/4)x − 9/4.

So the solution is all points on that line: {(x, (7/4)x − 9/4) | x ∈ R} (infinitely many solutions).