Question

Solve by graphing u=v and 6u=2v-24

Answer 1

Answer:

$u=-6 \\ \\ v=-6$

Step-by-step explanation:

In this exercise, we have two equations, namely:

$u=v \ and \ 6u=2v-24$

And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

$u=y \\ \\ v=x$

Then:

$\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.$

So here we have two lines.

The first one is:

$\boxed{y=x}$

This line passes through the origin and has a slope $m=1$

The second one is:

$6y=2x-24 \\ \\ \therefore y=\frac{2x-24}{6} \\ \\ \therefore \boxed{y=\frac{1}{3}x-4}$

This line has a slope $m=\frac{1}{3}$ and cuts the y-axis at $b=-4$

By using graph tools, we get the graph shown below, then:

$x=-6 \\ \\ y=-6 \\ \\ \\ Since \ u=y \ and \ v=x, then: \\ \\ u=-6 \\ \\ v=-6$