https://file.aiquickdraw.com/mathbot/file/1729091219774zqqrgahk.jpg

The system of linear equations given in the image is:

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

We need to find the solution, which corresponds to the point where the two lines intersect. Let's solve it algebraically to determine the intersection point.

---

### Step 1: Set the equations equal to each other
Since both equations are equal to \(y\), we equate them:

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

### Step 2: Solve for \(x\)
Move the \(2x\) from the right side to the left side:

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

\[
-4x = 8
\]

Now, divide both sides by \(-4\):

\[
x = -2
\]

### Step 3: Substitute \(x = -2\) into one of the original equations
Let’s use the second equation \(y = 2x + 4\):

\[
y = 2(-2) + 4
\]

\[
y = -4 + 4 = 0
\]

---

### Step 4: Write the solution
The intersection point, and thus the solution to the system, is:

\[
\boxed{(-2, 0)}
\]

---

### Verification with the graph
Looking at the graph, the two lines indeed intersect at the point \((-2, 0)\), confirming that our algebraic solution is correct.

---

Do you have any further questions, or would you like additional details?

---

**Related questions:**
1. How do you graph linear equations by hand?
2. What methods exist for solving systems of linear equations?
3. What happens when two lines in a system are parallel?
4. How do you interpret a system with infinitely many solutions?
5. How can you check your solutions graphically and algebraically?

**Tip:** When solving systems of equations graphically, always double-check that both equations are in slope-intercept form for easier graphing.

What is the solution to the system of equations y = -2x - 4 and y = 2x + 4?

Learn how to solve the system of linear equations y = -2x - 4 and y = 2x + 4 by finding the point of intersection. This problem covers graphing and algebraic methods to find solutions to systems of equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation