Question

For your rock collection display, you want to have at most 25 samples.

Answer 1

Answer:

$\left \{ {y\leq 25-x} \atop {y\geq 3x}} \right.$

The graph is attached.

Step-by-step explanation:

Let be "x" the number of metamorphic samples and "y" the number of sedimentary samples.

You know that you want to  to have at most 25 samples, then:

$y\leq 25-x$

And you want to have at least 3 times as many sedimentary samples as

metamorphic samples, then:

$y\geq 3x$

Therefore, the system of  inequalities that model the situation is:

$\left \{ {y\leq 25-x} \atop {y\geq 3x}} \right.$

The y-intercept of the line $y=25-x$ is:

$y=25-(0)\\\\y=25$

And the x-intercept is:

$0= 25-x\\\\x=25$

Knowing this, you can graph the line

The y-intercept of the line $y= 3x$ is:

$y=3(0)\\\\y=0$

And the x-intercept is:

$0= 3x\\\\x=0$

Knowing this, you can graph the line.

Observe the graph attached, where the solution of the system of inequalities is the intersection of the regions.