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2 years ago

Which of the following is a solution of 4x + 2y ≤ 6?

Mathematics

1 answer:

cestrela7 [59]2 years ago

6 0

Answer:

D. (1,0)

Step-by-step explanation:

Just plug in each coordinate for x and y into 4x+2y and see which one is less than or equal to 6.

Lets go through all of the possible answers:

A. (0,4)

4(0) + 2(4) ≤ 6

0 + 8 ≤ 6

8 ≤ 6

This is false. 8 is not less than or equal to 6.

B. (5,0)

4(5) + 2(0) ≤ 6

20 + 0 ≤ 6

20 ≤ 6

This is false. 20 is not less than or equal to 6.

C. (5,7)

4(5) + 2(7) ≤ 6

20 + 14 ≤ 6

34 ≤ 6

This is false because 35 is not less than or equal to 6

D. (1,0)

4(1) + 2(0) ≤ 6

4 + 0 ≤ 6

4 ≤ 6

This is true, because 4 is less than 6.

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Which equation does the graph of the systems of equations solve?

Viktor [21]

Answer:

We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.

Step-by-step explanation:

From the given graph, it is clear that the two lines meet at the point (3, 2).

In other words,

at x =3, y = 2

Thus,

The point of intersection between two lines is:

(x, y) = (3, 2)

Here:

x = 3 is the value of the x-coordinate

y = 2 is the value of the y-coordinate

Now, checking the equation i.e. 1/3x+1=2x-4 to determine whether the equation contains the correct value of x-coordinate or not.

$\frac{1}{3}x+1=2x-4$

Subtract 1 from both sides

$\frac{1}{3}x+1-1=2x-4-1$

Simplify

$\frac{1}{3}x=2x-5$

subtract 2x from both sides

$\frac{1}{3}x-2x=2x-5-2x$

Simplify

$-\frac{5}{3}x=-5$

Multiply both sides by 5

$3\left(-\frac{5}{3}x\right)=3\left(-5\right)$

Simplify

$-5x=-15$

Divide both sides by -5

$\frac{-5x}{-5}=\frac{-15}{-5}$

Simplify

$x=3$

Therefore, the value of x = 3

Conclusion:

We conclude that option 'C' i.e. 1/3x+1=2x-4 is the correct option.

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Step-by-step explanation:

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Step-by-step explanation:

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