# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x+y=2# and #2x-y=1#?

##### 1 Answer

Please refer to the graph and the explanation.

#### Explanation:

We are given systems of two linear equations in two variables:

These can be visually represented by simultaneously graphing both the equations.

The system can be **Consistent** or Inconsistent and the equations in the system can either be **Dependent** or **Independent.**

A system which has **No Solutions** are said to be **Inconsistent**.

A system with **one or more solutions** are called **Consistent**, having either one solution or an infinite number of solutions.

We are given systems of two linear equations in two variables:

If you refer to the graph available with this solution, you can observe two distinct intersecting straight lines: one

We get a pair of **single unique solution** for the system of equations.

As you can observe, the intersection point has coordinates

Our system of equations is therefore a **Consistent System of Independent Equations**.

The **solution set has single ordered pair #(1,1)#**

We will write our equations in the **Slope-Intercept Form:**

**Slope-Intercept Form** is written as

**Slope** and **y_intercept**

We can write

We can write

We observe that, using

The **Slope** is different from each equation.

The system has **One Solution** and therefore is a **Consistent System**.

The equations are also **Independent**, as each equation is describing a different straight line.

I hope this helps.