Question

Verify that your point from Question 2 is a solution to 2x-y=-12x−y=−1 AND is also a solution to y=5x-5y=5x−5. What does it mean if your point is a solution to both?

(The point is (2,5))

Answer 1

(a) Verified

(b) They are simultaneous equations

Explanation:

Given

`2x - y = -1`

`y =5x - 5`

Required

Verify that:
`(x,y) = (2,5)` is a solution

We have:

`2x - y = -1`

Substitute:
`(x,y) = (2,5)`

`2 * 2 - 5 = -1`

Evaluate all products

`4 - 5 = -1`

Subtract:

`-1 = -1`

Because both sides of the equation are equal, then the point is a solution

Also:
`y =5x - 5`

Substitute:
`(x,y) = (2,5)`

`5 = 5 * 2 - 5`

Evaluate all products

`5 = 10 - 5`

Subtract:

`5 = 5`

Because both sides of the equation are equal, then the point is a solution

Because the given point is a solution to both equations, then they are simultaneous equation