Question

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

You want to have at least 3 times as many sedimentary samples as
metamorphic samples.
Write and graph a system of inequalities to model the situation.​

Answer 1

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

The graph is attached.

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.