https://file.aiquickdraw.com/mathbot/file/1725710636921kh2eda1j.jpg

I see that you’ve uploaded an image of a system of equations. Let me transcribe and solve it for you.

The system of equations shown in the image is:

\[
\begin{aligned}
1. \quad 3x + 4y + z &= 1 \\
2. \quad 2x + 3y &= 0 \\
3. \quad 4x + 3y - z &= -2
\end{aligned}
\]

### Step-by-Step Solution:

#### Step 1: Solve Equation (2) for \(x\)
The second equation is \(2x + 3y = 0\), which can be solved for \(x\) as follows:

\[
2x = -3y \quad \Rightarrow \quad x = \frac{-3y}{2}
\]

#### Step 2: Substitute \(x = \frac{-3y}{2}\) into Equations (1) and (3)

Now substitute this expression for \(x\) into equations (1) and (3).

**Substitute into Equation (1):**
\[
3\left(\frac{-3y}{2}\right) + 4y + z = 1
\]
\[
-\frac{9y}{2} + 4y + z = 1
\]
Multiply everything by 2 to eliminate the fractions:
\[
-9y + 8y + 2z = 2
\]
Simplifying:
\[
-y + 2z = 2 \quad \Rightarrow \quad y = 2z - 2 \quad \text{(Equation 4)}
\]

**Substitute

Find all solutions to the following system of equations: 3x + 4y + z = 1, 2x + 3y = 0, 4x + 3y - z = -2.

This example demonstrates how to solve a system of linear equations with three variables using substitution and elimination methods. The problem involves the equations 3x + 4y + z = 1, 2x + 3y = 0, and 4x + 3y - z = -2. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation