/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 Solve each equation for \(y\). ... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 54

Solve each equation for \(y\). \(-2 x+y=9\)

Short Answer

Expert verified
y = 2x + 9

Step by step solution

01

Identify the equation

The given equation is \(-2x + y = 9\)
02

Isolate the variable y

To isolate \(y\), add \(2x\) to both sides of the equation:\(-2x + y + 2x = 9 + 2x\)
03

Simplify the equation

Combine like terms:\(y = 2x + 9\)

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Key Concepts

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

solving for a variable
Solving for a variable in an equation means finding the value of that variable that makes the equation true. In this exercise, we are asked to solve for \(y\).
This means we need to rewrite the equation in a way that expresses \(y\) alone on one side of the equation. This can involve several steps such as isolating the variable, combining like terms, and performing arithmetic operations on both sides of the equation.
Let's dive deeper into these steps one by one!
isolating the variable
Isolating the variable means getting the variable you are solving for by itself on one side of the equation.
For our equation \(-2x + y = 9\), we want to isolate \(y\). To do this, we need to move all other terms to the opposite side of the equation.
Here鈥檚 what this looks like:
  • Add \(2x\) to both sides of the equation:
    \(-2x + y + 2x = 9 + 2x\)
  • The equation simplifies to:
    \(y = 2x + 9\)
Now, \(y\) is isolated because it is by itself on the left side of the equation.
combining like terms
Combining like terms is a key step in simplifying equations. Like terms are terms that have the same variables raised to the same power.
In our exercise, we need to simplify the equation after isolating \(y\).
After adding \(2x\) to both sides of the equation, we get: \(-2x + y + 2x = 9 + 2x\).
Notice that \(-2x\) and \(2x\) are like terms because they both have the variable \(x\) raised to the same power.
Combining these like terms gives us: \(y = 2x + 9\).
This step simplifies the equation and makes it easier to solve for \(y\).

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Most popular questions from this chapter

Solve each system by the elimination method. $$ \begin{aligned} &0.5 x+3.4 y=13\\\ &1.5 x-2.6 y=-25 \end{aligned} $$

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