2a) x = 77 - 2y (option A)
2b) y = 77/2 - x/2
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:
[tex]\begin{gathered} \frac{4y}{4}\text{ = }\frac{1}{4}(154\text{ - 2x)} \\ y\text{ = }\frac{154}{4}\text{ - }\frac{2x}{4} \\ y\text{ = }\frac{77}{2}-\frac{x}{2} \end{gathered}[/tex]