Problem 44 Find $y$ given that $x=3$. ... [FREE SOLUTION]

Chapter 2: Problem 44

Find $y$ given that $x=3$. $$x-y=7$$

Short Answer

Expert verified

When $x = 3$, $y = -4$.

Step by step solution

Understand the given equation

The problem gives the equation for the relationship between the variables: $x - y = 7$ We are asked to find the value of $y$ when $x = 3$.

Substitute the value of x

Replace $x$ with 3 in the equation. So, the equation becomes:$3 - y = 7$

Solve for y

To find $y$, we need to isolate it on one side of the equation. Rearrange the equation:$3 - 7 = y$Solve for $y$:$y = -4$

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Key Concepts

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

equation solving

Solving an equation involves finding the value of unknown variables that make the equation true. In our exercise, we are given a linear equation with two variables, x and y. The goal is to find the value of y when x is provided. Linear equations generally form a straight line when plotted on a graph. They are some of the simplest types of equations and are foundational in algebra. In the given problem, the equation is:
1. Note the given equation:

Identify the variables: x and y
Understand the relationship defined by the equation: x - y = 7

This means that whatever values x and y might take, their difference must always be 7.
Our task is to solve this equation for y when x is specified as 3.

substitution method

The substitution method is a technique used to solve equations by replacing one variable with a known value. In solving our exercise, this method is essential since we need to insert the given value of x into the equation. Here鈥檚 how substitution works:
1. Substitute the known value:

Given: x = 3
Original equation: x - y = 7
Substitute x with 3: 3 - y = 7

This replacement helps simplify the equation, making it easier to solve for y.
The main advantage of the substitution method is its simplicity. It鈥檚 a straightforward approach to reducing the number of variables in an equation, which simplifies solving it.

isolating variables

Isolating the variable is the process of getting a variable alone on one side of the equation to solve for it. This is a crucial step in many algebraic problem-solving techniques. In our exercise, since we substituted x with 3, our equation became:
3 - y = 7
To isolate y, we need to rearrange the equation:

First, look at what is on the same side as y. We have 3 being subtracted by y.
To isolate y, we subtract 3 from both sides: 3 - 3 - y = 7 - 3
Simplify it: - y = 4
Since we need y, not -y, we multiply both sides by -1: y = -4

So, y equals -4. Isolating variables is a systematic approach to simplify equations and it is highly useful across various types of algebraic problems.

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91影视

Find \(y\) given that \(x=3\). $$x-y=7$$

Short Answer

Step by step solution

Understand the given equation

Substitute the value of x

Solve for y

Key Concepts

equation solving

substitution method

isolating variables

One App. One Place for Learning.

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