the tables represent two linear functions in a system. what is the solution to this system?

Explanation:

Step1: Find the slope - intercept form ($y = mx + b$) for the first function.

The $y$-intercept $b$ of the first function is the value of $y$ when $x = 0$, so $b_1=10$. The slope $m_1=\frac{y_2 - y_1}{x_2 - x_1}=\frac{18 - 26}{-2-(-4)}=\frac{-8}{2}=-4$. So the first function is $y=-4x + 10$.

Step2: Find the slope - intercept form for the second function.

The $y$-intercept $b$ of the second function is the value of $y$ when $x = 0$, so $b_2 = 2$. The slope $m_2=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8 - 14}{-2-(-4)}=\frac{-6}{2}=-3$. So the second function is $y=-3x + 2$.

Step3: Set the two functions equal to each other to find the $x$-value of the solution.

$-4x + 10=-3x + 2$. Add $4x$ to both sides: $10=x + 2$. Subtract 2 from both sides: $x = 8$.

Step4: Find the $y$-value of the solution.

Substitute $x = 8$ into the second function $y=-3x + 2$. $y=-3\times8+2=-24 + 2=-22$.

Answer:

$(8,-22)$