Question

The tables represent two linear functions in a system.

What is the solution to this system?

Answer 1

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)

Answer 2

Answer:

(8,-22)

Step-by-step 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 :$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute the values :

$y-26=\frac{18-26}{-2+4}(x+4)$

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

$y-26=-4x-16$

$y=-4x-16+26$

$y=-4x+10$ ---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 :$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute the values :

$y-14=\frac{8-14}{-2+4}(x+4)$

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

$y-14=-3x-12$

$y=-3x+2$ ---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)