Question

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

Answer 1

Answer:

the answer is no solutions

Step-by-step 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