Question

The tables represent two linear functions in a system.

What is the solution to this system?

Answer 1

(8,-22)

Explanation:

Table 1)

To form equation we will use two point slope form

`(x_1,y_1)=(-4,26)\\(x_2,y_2)=(-2,18)`

Formula :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values :

`y-26=(18-26)/(-2+4)(x+4)`

`y-26=-4(x+4)`

`y-26=-4x-16`

`y=-4x-16+26`

`y=-4x+10` ---1

Table 2)

To form equation we will use two point slope form

`(x_1,y_1)=(-4,14)\\(x_2,y_2)=(-2,8)`

Formula :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values :

`y-14=(8-14)/(-2+4)(x+4)`

`y-14=-3(x+4)`

`y-14=-3x-12`

`y=-3x+2` ---2

Now we are supposed to solve 1 and 2

Substitute the value of y from 1 in 2

`-4x+10=-3x+2`

`8=x`

Substitute the value of x in 2

`y=-3(8)+2`

`y=-22`

Hence the solution to this system is (8,-22)

Answer 2

The solution to this system is (x, y) = (8, -22).

The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).

You can extend each table after the same pattern.

In table 1, x-values increase by 2 and y-values decrease by 8.

In table 2, x-values increase by 2 and y-values decrease by 6.

The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...

... (x, y) = (8, -22)