Question

Y=15x+2

-15x+y=1

Is it one solution,no solution or infinite solution? Show work please :)

(50 points!!)

Answer 1

Since slopes are same. and y intercept is different, the system has no solution.

Explanation:

When dealing with linear equations, put the equation in slope intercept form,

`y = mx + b`

unless not asked to.

Equation 1 is in slope intercept form, but the second one isn't

`- 15x + y = 1`

Isolate y.

`y = 15x + 1`

So our equations is

`y = 15x + 1`

`y = 15x + 2`

Notice how the slope is the same and the y intercept is different.

This means s the system will never have a consistent system.

Why? The y intercept gives us the a distinct place for our linear equations.

If two places start in a different place, and have a constant slope, they will never intersect which thus forms a solution.

So the answer is no solution.

Answer 2

• No solutions.

Explanation:

Let's organize both equations.

• y = 15x + 2 (Organized)
• -15x + y = 1
• => y = 15x + 1 (Organized)

We now know that the organized equations are y = 15x + 1 and y = 15x + 2

We can see that their slopes are same. However, it's y-intercepts are different. These equations form parallel lines which basically means that these equations have no solutions. Please check out my graph to learn more.