Q16. - Algebra 1

Question

Solve each equation for y.

$3x+4y=10$

Step-by-Step Solution

Answer

The equation for y is $y=\frac{10-3x}{4}$.

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 similar sign 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 $3x+4y=10$ 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 both sides by 3x.

$\begin{array}{c}3x+4y-3x=10-3x\\ 4y=10-3x\end{array}$

Step 3. Simplify further for y .

Now to further simplify divide both sides by 4.

$\begin{array}{c}4y=10-3x\\ \frac{4y}{4}=\frac{10-3x}{4}\\ y=\frac{10-3x}{4}\end{array}$