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

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

User Sky Sanders
by
2.8k points

2 Answers

16 votes
16 votes

Answer:

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!

User Zaria
by
2.9k points
23 votes
23 votes

Answer:

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

User Andy Hin
by
2.8k points