Question

What is the solution to the system of equations? 2x – y = 7 y = 2x + 3

Answer 1

the answer is no solutions

Explanation:

the solution is found at the point in which the two lines intersect.

in this case they do not intersect because the lines are parallel. if you rearrange 2x – y = 7 you will get y = 2x - 7. the slope is 2x

the slope of the second equation is 2x as well. when slopes are the same they are parallel and therefore never cross.

Answer 2

For this case we have the following system of equations:

`2x-y = 7\\y = 2x + 3`

To solve, we substitute the second equation in the first:

`2x- (2x + 3) = 7\\2x-2x-3 = 7\\-3 = 7`

As noted, equality is not fulfilled. Thus, the system has no solution.

It can also be observed that the equations are:

`y = 2x + 3\\y = 2x-7`

That is, they have the same slope,
`m = 2`, so the lines are parallel. If the lines are parallel, they never intersect.

Answer:

The system has no solution