Question

The graph of 4x + 5y = 20 is shown on the grid. Which points are the solution set of 4x + 5y < 20? select two correct answers.

(2,2)
(4,0)
(-3,1)
(5,4)
(5,0)

Thank you in advance!!

Answer 1

solutions = (-3,1), (2,2)

Step-by-step explanation:

First solve for y=mx + b form but with the <

4x+5y < 20

5y < -4x+20

y < (-4/5)x+4

graph it (4 is the y-intercept and slope is -4/5)

because the sign is < you shade below

because its < instead of <= anything on the line is not a solution

anything in the shaded is a solution

solutions = (-3,1), (2,2)

Also helpful tip:

whenever dividing/multiplying a negative number over the sign flips (< to >)or (> to <)

Answer 2

The points that are part of the solution set for the inequality 4x + 5y < 20 are (2,2) and (-3,1) because when substituted into the inequality, they result in quantities less than 20, thus satisfying the inequality.

Step-by-step explanation:

To determine which points are part of the solution set for the inequality 4x + 5y < 20, each point must satisfy the inequality when substituted into the equation.

• For the point (2,2), substituting into the inequality we get 4(2) + 5(2) = 8 + 10 = 18, which is less than 20, so (2,2) is part of the solution set.
• For the point (-3,1), substituting into the inequality we get 4(-3) + 5(1) = -12 + 5 = -7, which is less than 20, so (-3,1) is also part of the solution set.

The other points do not satisfy the inequality and are therefore not part of the solution set. For instance, (4,0) gives 4(4) + 5(0) = 16 + 0 = 16, which is equal to 20, not less than, and this actually lies on the boundary line rather than in the solution region. Similarly, (5,4) and (5,0) do not satisfy the inequality.