Question

5x−y=3
−5x+2y=4
Which ordered pair satisfies the system of equations shown above?

Answer 1

`(2, 7)`

Explanation:

We can solve this system of equations by using elimination.

In this case, we can eliminate x by adding the two equations:

`5x+(-5x)-y+2y=3+4\\5x-5x+y=7\\y=7`

Then, substitute 7 for y to solve for x:

`5x-y=3\\5x-7=3\\\text{Add 7 to both sides}\\5x=10\\\text{Divide both sides by 5}\\x=2`

Substitute both these values into the system to check our answer:

`5x-y=3\\5(2)-7=3\\10-7=3\\3=3\rightarrow \text{correct!}`

`-5x+2y=4\\-5(2)+2(7)=4\\-10+14=4\\4=4\rightarrow \text{correct!}`

Therefore the ordered pair is:

`(x, y)=(2, 7)`