Question

Which shows the graph of the solution set of 2x+3y≤6?

Answer 1

we have

`2x+3y \leq 6`

Using a graphing tool

see the attached figure

The solution is the shaded area below the solid line

The answer in the attached figure

Answer 2

Option (a) is correct.

Explanation:

Given : equation 2x + 3y ≤ 6

We have to choose out of given option the graph that shows the graph of the solution set of 2x + 3y ≤ 6

Consider the given equation 2x + 3y ≤ 6

We first find the points where the equation cut x- axis and y-axis.

Thus,

For x - axis put y = 0 ,

We get 2x + 3(0) ≤ 6 ⇒ 2x ≤ 6 ⇒ x ≤ 3

Thus, point (3,0)

For y - axis put x = 0 ,

We get 2(0) + 3y ≤ 6 ⇒ 3y ≤ 6 ⇒ y ≤ 2

Thus, point (0,2)

For region we choose a test point and find the value of x and y on that test point and check whether it satisfy the inequality satisfies or not.

Consider the point (0, 0) , then inequality becomes,

2(0) + 3(0) ≤ 6 ⇒ 0 ≤ 6 (true)

Hence, region below the line will be considered.

Thus, Option (a) is correct.