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)

Explanation:

Step1: Find the equation of the first line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the first table with points $(x,y)$: When $x = 0,y = 2$, so $b = 2$. The slope $m=\frac{\Delta y}{\Delta x}=\frac{10 - 2}{2-0}=\frac{8}{2}=4$. So the equation of the first line is $y = 4x+2$.

Step2: Find the equation of the second line

For the second table, when $x = 0,y=- 4$, so $b=-4$. The slope $m=\frac{\Delta y}{\Delta x}=\frac{-2+4}{2 - 0}=\frac{2}{2}=1$. So the equation of the second line is $y=x - 4$.

Step3: Solve the system of equations

Set $4x+2=x - 4$. Subtract $x$ from both sides: $4x - x+2=x - x - 4$, which gives $3x+2=-4$. Subtract 2 from both sides: $3x+2 - 2=-4 - 2$, so $3x=-6$. Divide both sides by 3: $x=-2$. Substitute $x = - 2$ into $y=x - 4$, we get $y=-2 - 4=-6$.

Answer:

$(-2,-6)$