Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `8x - 5y - 30` and `5y - 8x = - 30`?

Answer 1

Infinitely many solutions & system is consistent

Explanation:

The given equations of straight lines `8x-5y=30` & `-8x+5y=-30` or `8x-5y=30` represent two straight lines which are exactly the coincident i.e. they represent same straight line hence there are infinite points of intersection hence the infinite number of solutions.

The system is consistent.

One can easily plot `8x-5y=30` using intercept form of straight line

`\frac{x}{30/8}+\frac{y}{-30/5}=1`

`\frac{x}{15/4}+\frac{y}{-6}=1`

The above line intersects the coordinate axes at the point `(15/4, 0)` & `(0, -6)` Locate these points on the coordinate axes & join them by a straight line to get the graph/plot