Question

The tables represent two linear functions in a system.

What is the solution to this system?

(1, 0)
(1, 6)
(8, 26)
(8, –22)

Answer 1

lets use one of formulas of linear functions:

y = kx + n

Now we need to find k and n for both linear functions. We do that by using table

We need only 2 values of x and 2 coresponding values of y to find k and x for one equation.

Function 1:
10 = k*0 + n which means n1 = 10
2 = k*2 + 10
2k = -8
k1 = -4

Function 2
2 = n2 ( we used values of 3rd row because x = 0 there and we can find n straight away)

-4 = 2k + 2
2k = -6
k2 = -3

Our system is now:

y = -4x + 10
y = -3x + 2
if we subtract second from first we get:
-4x + 3x + 10 - 2 = 0
-x + 8 = 0
x = 8

y = -3*8 + 2 = -22

Answer is (8,-22)