How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x=5y# and #2y=6x+10#?
1 Answer
Please see below.
Explanation:
Just draw the graphs of the two linear equations in two variables representing lines

If the two lines intersect, the point of intersection is the solution. In such a case we have a consistent solution.

If the two lines are parallel, they do not intersect and hence there is no solution. In such a case, we also say equations are inconsistent .

In the present case observe that
#3x=5y# and moving#x# and#y# on opposite sides, we get#y=5+3x# and multiplying each side by#2# , we get#2y=6x+10# , which is the equation of the other line.
Hence, the two equations represent the same line. In such a case one can say that the two lines are coincident i.e. they intersect at infinite solutions represented by
graph{5+3x [20, 20, 10, 10]}