Question

solve each of the following equations for the variable “y”

1. 2y = 4x + 10
2. 2x + 4y = -22
3. 8y - 4x = 2
4. -5y + 15 = 3x
5. 18 = 3y - 12x
6. 19 = 7x + y

Explanation:

Step1: Isolate y in 2y = 4x + 10

Divide both sides by 2. So $y=\frac{4x + 10}{2}=2x + 5$.

Step2: Isolate y in 2x + 4y=-22

First, subtract 2x from both sides: $4y=-2x - 22$. Then divide by 4: $y=\frac{-2x - 22}{4}=-\frac{1}{2}x-\frac{11}{2}$.

Step3: Isolate y in 8y - 4x = 2

Add 4x to both sides: $8y=4x + 2$. Then divide by 8: $y=\frac{4x + 2}{8}=\frac{1}{2}x+\frac{1}{4}$.

Step4: Isolate y in -5y + 15 = 3x

Subtract 15 from both sides: $-5y=3x - 15$. Then divide by -5: $y=\frac{3x - 15}{-5}=-\frac{3}{5}x + 3$.

Step5: Isolate y in 18 = 3y - 12x

Add 12x to both sides: $3y=12x + 18$. Then divide by 3: $y = 4x+6$.

Step6: Isolate y in 19 = 7x + y

Subtract 7x from both sides: $y=19 - 7x$.

Answer:

1. $y = 2x+5$
2. $y=-\frac{1}{2}x-\frac{11}{2}$
3. $y=\frac{1}{2}x+\frac{1}{4}$
4. $y=-\frac{3}{5}x + 3$
5. $y = 4x+6$
6. $y=19 - 7x$