Question

8. Is (5,6) a solution to the following system? How do you know?
3x +2y = 27
x = y +1

Answer 1

It is not a solution.

Explanation:

First, as we know what x is equal to, substitute the second equation into the first:

3x + 2y = 27

3(y + 1) + 2y = 27

3y + 3 + 2y = 27

5y + 3 = 27

Subtract 3 from both sides:

5y + 3 - 3 = 27 - 3

5y = 24

Divide both sides by 5:

`(5y)/(5) = (24)/(5)`

So
`y= (24)/(5)`

At this point we know that (5, 6) is not a solution to the system because this should be the y value (6). To confirm this we will calculate x by substituting in the known y in the second equation:

x = y + 1

x =
`(24)/(5) + 1`

`x = (29)/(5)`

Further proving that (5,6) is not a solution.

Hope this helps!