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Chapter 3: Problem 72

Solve the equation. $$13 y-10 y=-18$$

Short Answer

Expert verified
y = -6

Step by step solution

01

Combine Like Terms

Combine the terms involving the variable y. So, combine the terms \(13y\) and \(-10y\).
02

Simplify the Equation

After combining like terms, the equation becomes \(3y = -18\).
03

Solve for y

Divide both sides of the equation by 3 to isolate the variable y. Thus, \(y = \frac{-18}{3}\).
04

Simplify the Result

Simplify \(\frac{-18}{3}\) to find the value of y. This gives \(y = -6\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining Like Terms
Combining like terms is a fundamental step in solving linear equations. In your equation, you have terms that both include the variable y, which are 13y and -10y. To combine these, add or subtract the coefficients (the numbers in front of y) together while keeping the variable part the same. So, you'll calculate 13 - 10 to get 3. Here, you end up with 3y. This step simplifies the equation and makes it easier to solve. Remember, only like terms, or terms that have the same variable, can be combined this way.
Simplify
Once you've combined like terms, the next step is to simplify the equation. In this exercise, combining 13y and -10y gives you 3y. So, the equation now reads 3y = -18. Simplifying an equation often means reducing it to a more straightforward form. This is crucial because it allows you to more easily isolate the variable later on. By ensuring the equation is as simple as possible, you minimize the complexity and potential errors in further steps.
Isolate the Variable
To solve for y, you need to isolate the variable on one side of the equation. In the equation 3y = -18, y is currently being multiplied by 3. To isolate y, you must 'undo' the multiplication. This is done by performing the opposite operation, which in this case is division. By dividing both sides of the equation by 3, you are left with y on one side. As a rule of thumb, always apply the same operation on both sides to maintain balance in the equation. This step is crucial for finding the value of the unknown variable.
Division in Equations
Division is a key operation when solving linear equations. Once the equation is simplified and involves a multiplication, as in 3y = -18, you divide both sides by the coefficient of the variable (which is 3 in this case). So, you calculate \(\frac{-18}{3} \). This gives you y = -6. Always ensure you're dividing correctly and simplifying accurately. Division helps you isolate the variable and find its precise value. It鈥檚 an essential part of getting to the final solution accurately.

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