# How do you solve the system #y=2x+6# and #2x-y=2# using substitution?

##### 3 Answers

The two lines have the same slope, therefore they are parallel and there is no solution.

#### Explanation:

Solve the system of equations:

**Equation 1:**

**Equation 2:**

If Equation 2 is converted from standard form to slope-intercept form, you will see that both lines have the same slope, and are therefore parallel lines, and there is no solution.

**Equation 2**

Subtract

Divide both sides by

So both lines have the same slope of

graph{(y-2x-6)(2x-y-2)=0 [-16.83, 5.67, -19.26, -8.01]}

There is no solution to the equations.

#### Explanation:

We are given two equations, one of which has

Substitute the expression

This is obviously false and there is no

This is an indication that there is no possible solution to this equation.

On closer inspection you should notice that both equations represent equations of straight lines:

The lines have the same slope which means they are parallel and therefore will never intersect, hence confirming the answer we obtained before.

No solutions- equations never intersect (parallel lines)

#### Explanation:

First, let's convert our second equation into slope-intercept form

Let's subtract

Next, divide all terms by

We see that our slope, the coefficient on the

It is important to realize that when two lines have the same slope, it means they are parallel. **This means they never intersect**.

Since they never intersect, it means this system has no solution.

Hope this helps!