Question

Here is an equation: `6x+2y=36`. 1. For each value of `x`, determine the value of `y`.

Answer 1

`x` is `0`, `y` is `18`.

Explanation:

To determine the value of `y` for each value of `x` in the equation `6x + 2y = 36`, we can solve for `y` by isolating it on one side of the equation.

1. Start by subtracting `6x` from both sides of the equation to move the `6x` term to the other side:

`2y = 36 - 6x`

2. Simplify the right side of the equation:

`2y = 36 - 6x`

3. Divide both sides of the equation by `2` to isolate `y`:

`y = (36 - 6x) / 2`

Now we have an expression for `y` in terms of `x`. By substituting different values for `x`, we can find the corresponding values of `y`.

For example, if we let `x` be `0`, we can calculate the corresponding value of `y`.

Answer 2

x = 6 - (1/3)y

Explanation:

We can solve for x in the equation:

6x + 2y = 36

with the following steps.

1) subtract 2y from both sides

6x = 36 - 2y

2) divide both sides by 6 (x's coefficient)

x = 6 - (2/6)y

3) reduce y's coefficient (2/6) to the lowest terms (1/3)

x = 6 - (1/3)y