Question

2. Here is a linear equation in two variables:2x + 4y - 31 = 1232a. Solve for x.*A. x = 77-2yB. x = 2y - 77C. x = 154 - 4yD. x = 154 - 2y2b. Solve for y."

Answer 1

2a) x = 77 - 2y (option A)

2b) y = 77/2 - x/2

Step-by-step explanation:

2a) 2x + 4y - 31 = 123

To solve for x, first we need to collect like terms

Add 31 to both sides:

2x + 4y - 31 + 31 = 123 + 31

2x + 4y = 154

Next we move 4y to the other side by subtracting 4y from both sides:

2x + 4y - 4y = 154 - 4y

2x = 154 - 4y

Divide both sides by 2:

2x/2 = 1/2 (154 - 4y)

x = 154/2 - 4y/2

x = 77 - 2y (option A)

2b) To solve for y using the first equation, we will collect like terms

2x + 4y - 31 = 123

Add 31 to both sides:

2x + 4y - 31 + 31 = 123 + 31

2x + 4y = 154

subtract 2x from both sides:

2x - 2x + 4y = 154 - 2x

4y = 154 - 2x

divide both sides by 4:

`\begin{gathered} (4y)/(4)\text{ = }(1)/(4)(154\text{ - 2x)} \\ y\text{ = }(154)/(4)\text{ - }(2x)/(4) \\ y\text{ = }(77)/(2)-(x)/(2) \end{gathered}`