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

It is not a solution.

Step-by-step 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:

So

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 =

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

Hope this helps!

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is