Question

In the equation below, a and b are constants. If a = b, what is the value of x in terms of y ? 2xa=8yb Select one:

A. 13y
B. 3y
C. 8y
D. y

Answer 1

3y

Explanation:

Cross multiply to simplify the equation.

2xa=8yb

2x(b)=8y(a)

Since a=b, substitute a for b in the right side of the equation. Then, divide both sides by a to eliminate it.

2x(b)=8y(a)

2x(a)a=<span>8y(a)a

2x=8y

Step 2:

Rewrite the right side of the equation to have a base of 2.

To solve for the value of x in terms of y, both sides of the equation need to have the same base. Therefore, 8 needs to be rewritten to have a base of 2. Since 8=23, substitute 23 for 8 in the equation.

2x=8y

2x=(23)y

Remember that when an exponent is raised to another exponent, the two exponents are multiplied.

2x=(23)y

2x=23y

From this relationship, it is clear that x=3y

Step 3:

Match your solution to the correct answer choice.

Select "3y" as your answer choice and move on to the next question.

Answer 2

Answer:
`x=4y`

Explanation:

The equation is
`2xa=8yb`.

To find the value of the variable "x" in terms of "y", you need to apply the Division property of equality and divide both sides of the equation by "2a". Then:

`(2ax)/(2a)=(8yb)/(2a)`

`x=(8yb)/(2a)`

You know that the costants "a" and "b" are equal (
`a=b`), then:

`(b)/(a)=1`

Knowingt this, you can simplify.

Therefore, you get that the value of "x" in terms of "y" is:

`x=4y`