Question

Solve each equation for the given variable.

$x+y=5$for$y$

Short answer

The equation for $y$is $y=5-x$.

Step-by-step solution

Step 1. State the concept used.

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Rewrite the equation to solve for y. 

In order to solve the given equation$x+y=5$for the variable, isolate the variable term $y$on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate$y$on both sides, first, subtract $x$ from both sides and then simplify furtheras shown below,

$$\begin{gathered} x+y=5 \\ x+y-x=5-x \end{gathered}$$

Step 3. Simplify further for y.

Simplify the equation and get,

$$\begin{gathered} x+y=5 \\ x+y-x=5-x \\ y=5-x \end{gathered}$$