Question

The graph shows the solution to a system of inequalities:

Which of the following inequalities is modeled by the graph?

A.

`4x + 3y \leqslant 12;x \geqslant 0`
B.

`4x + 3y \geqslant 12;x \geqslant 0`
C.

`4x - 3y \leqslant 12;x \geqslant 0`
D.

`- 4x - 3y \leqslant 12;x \geqslant 0`

​

Answer 1

Option A.
`4x+3y\leq 12` and
`x\geq 0`

Explanation:

we know that

The solution of the first inequality is the shaded area below the solid line
`4x+3y=12`

The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)

therefore

The first inequality is

`4x+3y\leq 12`

The solution of the second inequality is the shaded area to the right of the solid line x=0

therefore

The second inequality is

`x\geq 0`