Question

Is `(1,5)` a solution to the system of equations `y=x+10` and `y=3x+2`?

Answer 1

Not a solution

Explanation:

If this is a solution then `x = 1` and `y = 5` will satisfy each equation

Try `y = x+10`

Substitute `x = 1`

`y = 1 + 10 = 11`

Hence `y = 11`

Hence this does not hold, if we got 5, then we could try the second equation, and if that held, it is a solution, but it doesn't even satisfy the first equation, hence it is `color(red)(underline("not" )` a solution

Answer 2

It is a solution to the second equation only

Explanation:

substitute the numbers in and see

(1,5) into `y=x+10`

5=1+10
5=11
No

(1,5) into `y=3x+2`

5=3+2
5=5
Yes