Question

12. What is the solution of the system of equations?

y = - 2x + 5
y = -2x + 20
no solution
(1,3)
infinitely many solutions

Answer 1

no solution

Explanation:

Hi there!

We are given this system of equations:

y=-2x+5

y=-2x+20

and we want to find the solution (the point in which the lines intersect)

There are 3 ways to solve a system, but let's use substitution in this case

Both equations are set to y, so they should be equal to each other via a property known as transitivity (if a=b and b=c, then a=c)

-2x+5=-2x+20 (the same as y=y)

Now let's solve for x

add 2x to both sides

5=20

In this case, we got an untrue statement. If this happens, then the lines won't intersect.

If they won't intersect, there's no solution

Hope this helps!

Answer 2

no solutions

Explanation:

y = - 2x + 5

y = -2x + 20

Set the two equations equal

- 2x + 5 = -2x + 20

Add 2x to each side

- 2x+2x + 5 = -2x+2x + 20

5 = 20

This is never true so there are no solutions