# 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#?

##### 2 Answers

Dec 30, 2015

#### Explanation:

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

Therefore check if

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

In this case, the system is consistent as

Dec 30, 2015

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.