Question

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

Answer 1

Answer:

The graph in the attached figure

Step-by-step 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