Answer:
[tex]u=-6 \\ \\ v=-6[/tex]
Step-by-step explanation:
In this exercise, we have two equations, namely:
[tex]u=v \ and \ 6u=2v-24[/tex]
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:
[tex]u=y \\ \\ v=x[/tex]
Then:
[tex]\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.[/tex]
So here we have two lines.
The first one is:
[tex]\boxed{y=x}[/tex]
This line passes through the origin and has a slope [tex]m=1[/tex]
The second one is:
[tex]6y=2x-24 \\ \\ \therefore y=\frac{2x-24}{6} \\ \\ \therefore \boxed{y=\frac{1}{3}x-4}[/tex]
This line has a slope [tex]m=\frac{1}{3}[/tex] and cuts the y-axis at [tex]b=-4[/tex]
By using graph tools, we get the graph shown below, then:
[tex]x=-6 \\ \\ y=-6 \\ \\ \\ Since \ u=y \ and \ v=x, then: \\ \\ u=-6 \\ \\ v=-6[/tex]
