Question

Which point is a solution to this system of inequalities?
y < 1/2x – 3
y + 2x > 6

Answer 1

Answer:   C. (5, -2)

Step-by-step explanation:

Graph each equation:

Equation 1: y < (1/2)x - 3 -->  m = (1/2)  b = -3,   dashed line,   shaded below

Equation 2: y > -2x + 6 -->  m = -2  b = 6,   dashed line,   shaded above

or  plug the values into the equations.  It must be TRUE for both equations:

               y < (1/2)x - 3         y > -2x + 6

(7, -8)            True                   False

(2, -3)            True                   False

(5, -2)            True                   True           <-- This works!

(4, 1)             False                  True

Answer 2

Inequalities help us to compare two unequal expressions. The correct option is C.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For a point to be the solution of the system of inequalities, the point when substituted in the inequalities must satisfy both the given inequalities.

A. (7, -8)

y < 1/2x – 3

-8 < (1/2)7 - 3

-8 < 0.5

y + 2x > 6

-8 + 2(7) > 6

-8 + 14 > 6

6 > 6

Since the second inequality is not satisfied, therefore, the given point is not the solution.

B. (2, -3)

y < 1/2x – 3

-3 < (1/2)2 - 3

-3 < -2

y + 2x > 6

-3 + 2(2) > 6

-3 + 4 > 6

1 > 6

Since the second inequality is not satisfied, therefore, the given point is not the solution.

C. (5, -2)

y < 1/2x – 3

-2 < (1/2)5 - 3

-3 < -2

y + 2x > 6

-2 + 2(5) > 6

-2 + 10 > 6

8 > 6

Since both the inequality are satisfied, therefore, the given point is the solution.

D. (4, 1)

y < 1/2x – 3

1 < (1/2)4 - 3

1 < -1

Since the first inequality is not satisfied, therefore, the given point is not the solution.

Learn more about Inequality:

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