What is the y value of the intersection of x + y = 8 and x – 2y = -4 when solving by using the graphing method?

Mar 22, 2018

$y = 4$

Explanation:

First rearrange the two equations so $y$ is a function of $x$:

$x + y = 8 \to \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \textcolor{b l u e}{y = 8 - x} \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \left[1\right]$

$x - 2 y = - 4 \to \textcolor{b l u e}{y = \frac{1}{2} x + 2} \setminus \setminus \setminus \setminus \left[2\right]$

Because these are straight lines, we only need to put in two values of $x$ for each equation and then calculate the corresponding values of $y$.

$\left[1\right] \setminus \setminus \setminus \setminus$ $x = - 2 \setminus \setminus \setminus , x = 6$

$y = 8 - \left(- 2\right) = 10$

$y = 8 - \left(6\right) = 2$

So we have coordinates $\left(- 2 , 10\right)$ and $\left(6 , 2\right)$

$\left[2\right] \setminus \setminus \setminus \setminus$ $= - 4 \setminus \setminus \setminus$ , $x = 6$

$y = \frac{1}{2} \left(- 4\right) + 2 = 0$

$y = \frac{1}{2} \left(6\right) + 2 = 5$

So we have coordinates $\left(- 4 , 0\right)$ and $\left(6 , 5\right)$

We now plot each pair of coordinates and join them with a straight line.

You should have a graph that looks like this:

We can see from this that, at the intersection the $y = 4$