Question

3. Which graph best represents the solution to the following system? (1 point)
(5x – 2y <10

Answer 1

The graph in the attached figure

Explanation:

The complete question is

Which graph best represents the solution to the following system?

5x - 2y < (less than or equal to) 10

x + y < 5

we have

`5x-2y\leq 10` ----> inequality A

isolate the variable y

Adds 2y both sides

`5x \leq 10+2y`

Subtract 10 both sides

`5x-10 \leq 2y`

Divide by 2 both sides

`2.5x-5 \leq y`

Rewrite

`y \geq 2.5x-5`

The solution of the inequality A is the shaded area above the solid line

The equation of the solid line is
`y=2.5x-5`

The slope of the solid line is positive
`m=2.5`

The y-intercept of the solid line is (0,-5)

The x-intercept of the solid line is (2,0)

`x+y < 5` -----> inequality B

Isolate the variable y

Subtract x both sides

`y < -x+5`

The solution of the inequality B is the shaded area below the dashed line

The equation of the dashed line is
`y=-x+5`

The slope of the dashed line is negative
`m=-1`

The y-intercept of the dashed line is (0,5)

The x-intercept of the dashed line is (5,0)

using a graphing tool

The solution of the system of inequalities is the shaded area between the solid line and the dashed line

see the attached figure