https://file.aiquickdraw.com/mathbot/file/17254833039560s567spz.jpg

This is a system of two linear equations:

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

To solve this system of equations, we can use either substitution or elimination. Let's solve it using substitution, as both equations are already solved for \( y \).

### Step 1: Set the equations equal to each other
Since both equations are equal to \( y \), we can set the right-hand sides of the equations equal to each other:

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

### Step 2: Solve for \( x \)
To solve for \( x \), first add \( 2x \) to both sides:

\[
x + 2x + 2 = -2 \\
3x + 2 = -2
\]

Next, subtract 2 from both sides:

\[
3x = -4
\]

Finally, divide by 3:

\[
x = -\frac{4}{3}
\]

### Step 3: Solve for \( y \)
Now that we have \( x = -\frac{4}{3} \), we can substitute this value back into either of the original equations to find \( y \). Let's use the first equation \( y = x + 2 \):

\[
y = -\frac{4}{3} + 2
\]

Convert 2 to a fraction:

\[
y = -\frac{4}{3} + \frac{6}{3} = \frac{2}{3}
\]

### Final Answer:
The solution to the system is:

\[
\left( x, y \right) = \left( -\frac{4}{3}, \frac{2}{3} \right)
\]

Would you like more details or have any questions about the solution? Here are five related questions that you might find interesting:

1. How would you graph these two equations on the coordinate plane?
2. What is the significance of the point where these two lines intersect?
3. How can the elimination method be applied to this system?
4. What does the solution represent in real-world applications?
5. Can you find another pair of linear equations with the same solution?

**Tip:** When solving a system of equations, always check your solution by substituting the values back into the original equations.

Solve the system of linear equations: y = x + 2 and y = -2x - 2.

Learn how to solve the system of linear equations y = x + 2 and y = -2x - 2 with a detailed step-by-step solution. This problem involves key algebraic concepts such as substitution method and solving systems of equations, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation