# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x - 2y = 10# and #5x + 2y = 6#?

##### 1 Answer

The lines intersect at a single point, therefore the system of equations is consistent.

#### Explanation:

**Equation 1:**

**Equation 2** :

Both equations are in the standard form for a linear equation. This form makes it easy to determine the x- and y-intercepts. We can use those two points to graph each equation.

**X-intercept:** value of

Substitute

**Y-intercept:** value of

Substitute

**Equation 1**

**X-intercept:** Substitute

Divide both sides by

x-intercept:

**Y-intercept:** Substitute

Divide both sides by

y-intercept:

Draw a straight line through the two points. This is the graph for Equation 1.

**Equation 2**

**X-intercept:** Substitute

Divide both sides by

x-intercept:

**Y-intercept:** Substitute

Divide both sides by

y-intercept:

Draw a line between the two points. This is the graph of Equation 2.

The lines intersect at a single point, therefore the system of equations is consistent.

graph{(3x-2y-10)(5x+2y-6)=0 [-10, 10, -5, 5]}