Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `5x-5y=10` and `3x-6y=9`?

Answer 1

`x=1`
`y=-1`

Explanation:

Graph the 2 lines. A solution corresponds to a point that lies on both lines (an intersection).

Therefore check if

1. They have the same gradient (parallel, no intersection)
2. They are the same line (all points are solution)

In this case, the system is consistent as `(1,-1)` is a point of intersection.

Answer 2

There are three methods to solve this equation. I am using substitution method. this equation is consistent as a1/a2 is not = to b1/b2. It will have only 1 solution.

Explanation:

This is how we do this;
x=(10+5y)5 (from equation 1)
putting the value of x in equation 2
3(10+5y)5-6y=9
(30+15y)5-6y=9
30+15y-30y=45
30+(-15y)=45
-15y=15
y=-1
therefore, x=(10+5*-1)5
x=1
Hence solved.