/*! 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 104 Solve each equation for \(y\) ... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 104

Solve each equation for \(y\) $$ 3 x+y=6 $$

Short Answer

Expert verified
y = 6 - 3x

Step by step solution

01

Isolate the term with y

Start with the equation: \[ 3x + y = 6 \] Subtract \( 3x \) from both sides of the equation to isolate the term with \( y \): \[ y = 6 - 3x \]

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Key Concepts

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

Isolate the Variable
In solving linear equations, one common strategy is to isolate the variable. This means getting the variable you are solving for, by itself on one side of the equation.
In our example, we need to solve for y in: ewline ewline \[3x + y = 6 \]
To isolate y, we need to move all other terms to the opposite side of the equation. We do this by performing an operation that will cancel out \[3x \] on the left side.
Subtracting Terms
More often than not, isolating a variable involves subtracting terms.
In our problem, the term with x needs to be subtracted from both sides to isolate y:
\[3x + y - 3x = 6 - 3x \]
By subtracting \[3x \], the left side simplifies to just y:
\[y = 6 - 3x \]
Understanding Linear Equations
Linear equations are mathematical statements of equality that involve variables raised to the power of one. They are called linear because their graph is a straight line.
In our example:
\[3x + y = 6 \]
Notice that both terms 3x and y are to the power of one.
After isolating and manipulating the terms, we get:
\[y = 6 - 3x \]
This equation represents a straight line when plotted on a graph, with a slope of -3 and a y-intercept of 6.

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