# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #6x - 7y = 49# and #7y - 6x = -49#?

##### 1 Answer

#### Answer:

See a solution process below:

#### Explanation:

First, we need to graph each line by finding two solutions for each equation, plotting the solution points and then drawing a line through the points.

**Equation 1:**

**First Point:**#x = 0#

**Second Point:**#x = 7#

-**First Graph:**

graph{(x^2 + (y+7)^2 - 0.075)((x - 7)^2 + (y+1)^2 - 0.075)(6x - 7y - 49) = 0 [-20, 20, -10, 10]}

**Equation 2:**

**First Point:**#x = 0#

**Second Point:**#x = 7#

-**First and Second Graph:**

graph{(x^2 + (y+7)^2 - 0.075)((x - 7)^2 + (y+1)^2 - 0.075)(6x - 7y - 49) = 0 [-20, 20, -10, 10]}

**Solutoin:**

As we can see from the graph, both equations represent the same line. Therefore, there are an infinite number of solutions.

The lines are **Consistent** because there is at least one solution.