https://file.aiquickdraw.com/mathbot/file/1729547239500czn062vz.jpg

We are given a system of two linear equations:

\[
\begin{cases}
y = x - 2 \\
y = 4x + 1
\end{cases}
\]

### Step 1: Set the two equations equal to each other

Since both equations are already solved for \(y\), we can set them equal to each other:

\[
x - 2 = 4x + 1
\]

### Step 2: Solve for \(x\)

Now, solve the equation for \(x\):

1. Subtract \(x\) from both sides:
   \[
   -2 = 3x + 1
   \]

2. Subtract 1 from both sides:
   \[
   -3 = 3x
   \]

3. Divide both sides by 3:
   \[
   x = -1
   \]

### Step 3: Substitute \(x = -1\) back into one of the original equations

Substitute \(x = -1\) into either equation. Let's use the first equation:

\[
y = x - 2
\]
\[
y = -1 - 2 = -3
\]

### Final Solution:

The solution to the system is \(x = -1\) and \(y = -3\). Therefore, the solution is:

\[
(x, y) = (-1, -3)
\]

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you solve a system of equations using the elimination method?
2. What happens if a system of equations has no solution?
3. How can you graphically interpret the solution to this system?
4. How do you solve a system of non-linear equations by substitution?
5. How do systems of equations relate to real-world problems?

**Tip:** In substitution, always solve for one variable first and substitute it into the other equation for a systematic approach.

Solve each system by substitution. y = x - 2 and y = 4x + 1.

Learn how to solve the system of linear equations y = x - 2 and y = 4x + 1 using the substitution method. This example demonstrates a step-by-step approach to finding the solution by equating the two expressions for y, making it easy for students in Grades 8-10 to understand the core concepts of algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation