solving a system represented in a table\nthe tables represent two linear functions. the equation represented…

Explanation:

Step1: Find the slope of the second - table function

The slope $m$ of a linear function is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the second table, say $(x_1,y_1)=(-4,-5)$ and $(x_2,y_2)=(-3,-7.5)$. Then $m=\frac{-7.5-(-5)}{-3 - (-4)}=\frac{-7.5 + 5}{-3+4}=\frac{-2.5}{1}=-2.5$.

Step2: Find the y - intercept of the second - table function

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(-4,-5)$ and $m=-2.5$. So $y-(-5)=-2.5(x - (-4))$, which simplifies to $y + 5=-2.5(x + 4)$. Expand the right - hand side: $y+5=-2.5x-10$. Then $y=-2.5x-15$.

Step3: Solve the system of equations

We have the system of equations $y = 5.75x+34.5$ and $y=-2.5x - 15$. Set them equal to each other: $5.75x+34.5=-2.5x-15$. Add $2.5x$ to both sides: $5.75x+2.5x+34.5=-15$. Combine like terms: $8.25x+34.5=-15$. Subtract 34.5 from both sides: $8.25x=-15 - 34.5=-49.5$. Divide both sides by 8.25: $x=\frac{-49.5}{8.25}=-6$. Substitute $x = - 6$ into $y=-2.5x-15$, then $y=-2.5\times(-6)-15=15 - 15=0$.

Answer:

The linear equation represented by the second table is $y=-2.5x - 15$. The solution to the system of equations is $x=-6,y = 0$.