Question

PLS HELP ASAP

Which point is a solution to y≤−2x+3?
A. (0,4)
B. (1,0)
C. (3,−2)
D. (5,−2)

Answer 1

We are asked to determine which of these points is a solution to the following inequality:

`\mapsto\quad\bf{y\leqslant-2x+3}`

`\mathbb{EXPLANATION:}`

First, we are going to determine the x- and y-coordinates for each point.

Point 1:

The x-coordinate is 0; the y-coordinate is 4.

Point 2:

The x-coordinate is 1, and the y-coordinate is 0.

Point 3:

The x-coordinate is 3, and the y-coordinate is -2.

Point 4:

The x-coordinate is 5, and the y-coordinate is -2.

Now, we know that number to plug into the inequality.

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For the first point:

Plug in 0 for x and 4 for y, like this:

`\longmapsto\quad\bf{4\leqslant-2(0)+3}`

Then, evaluate.

`\longmapsto\quad\bf{4\leqslant0+3}`

`\longmapsto\quad\bf{4\leqslant3}`

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This ordered pair is not a solution to the inequality.

Let's try the next one, (1,0).

`\longmapsto\quad\bf{0\leqslant-2(1)+3}`

`\longmapsto\quad\bf{0\leqslant-2+3}`

`\longmapsto\quad\bf{0\leqslant1}`

This ordered pair is a solution.

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Let's do the third one, (3,-2).

`\longmapsto\quad\bf{-2\leqslant-2(3)+3}`

`\longmapsto\quad\bf{-2\leqslant-6+3}`

`\longmapsto\quad\bf{-2\leqslant-3}`

Not a solution!

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And finally, let's try (5,-2).

`\longmapsto\quad\bf{-2\leqslant-2(5)+3}`

`\longmapsto\quad\bf{-2\leqslant-10+3}`

`\longmapsto\quad\bf{-2\leqslant-7}`

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Conclusion

The solution to the inequality y ≤ -2x + 3 is (1,0).

Answer 2

B. (1,0)

Step-by-step explanation:

One method is to simply substitute values inside the inequality and check.

Given equation: y ≤ −2x+3

Like:

a. 4 ≤ -2(0) + 3

4 ≤ 3

b. 0 ≤ -2(1) + 3

0 ≤ 1

• (B) this statement is true

c. -2 ≤ -2(3) + 3

-2 ≤ -3

d. -2 ≤ -2(5) +3

-2 ≤ -7