2x+y-z=9 −𝑥+6𝑦+22=−17−*x*+6*y*+22=−17

5𝑥+7𝑦+2=45*x*+7*y*+2=4

It seems like the equations have some repeated and misformatted parts. Based on the patterns, I assume you intended a system of three equations. I'll simplify the equations as best I can interpret them. Here's what the system seems like:

1. \( 2x + y - z = 9 \) 
2. \(-x + 6y + 22 = -17\) 
3. \( 5x + 7y + 2 = 4\)

Let's simplify each equation:

### Simplified Equations:

1. From \( 2x + y - z = 9 \) — (Equation 1)  
   
2. From \(-x + 6y + 22 = -17\), simplify:
   \[ -x + 6y = -39 \]  — (Equation 2)

3. From \( 5x + 7y + 2 = 4 \), simplify:
   \[ 5x + 7y = 2 \] — (Equation 3)

Now we have:

1. \( 2x + y - z = 9 \)
2. \(-x + 6y = -39\)
3. \(5x + 7y = 2\)

### Solving the System of Equations

Let's solve these equations step by step.

1. From Equation 2:  
   \[ -x + 6y = -39 \implies x = 6y + 39 \]

2. Substitute \(x = 6y + 39\) into Equation 3:

   \[ 5(6y + 39) + 7y = 2 \]

   \[ 30y + 195 + 7y = 2 \]

   \[ 37y + 195 = 2 \]

   \[ 37y = 2 - 195 \]

   \[ 37y = -193 \implies y = -\frac{193}{37} = -\frac{193}{37} \approx -5.216 \]

3. Substitute \( y = -\frac{193}{37} \) back into the expression for \(x\):

   \[ x = 6\left(-\frac{193}{37}\right) + 39 \]

   \[ x = -\frac{1158}{37} + 39 \]

   \[ x = -\frac{1158}{37} + \frac{1443}{37} = \frac{285}{37} = 7.703 \]

4. Finally, use Equation 1 to find \(z\):

   Substitute \(x = \frac{285}{37}\) and \(y = -\frac{193}{37}\):

   \[ 2\left(\frac{285}{37}\right) + \left(-\frac{193}{37}\right) - z = 9 \]

   Simplify:

   \[ \frac{570}{37} - \frac{193}{37} - z = 9 \]

   \[ \frac{377}{37} - z = 9 \]

   \[ -z = 9 - \frac{377}{37} \]

   \[ -z = \frac{333}{37} - \frac{377}{37} = -\frac{44}{37} \]

   \[ z = \frac{44}{37} \approx 1.189 \]

### Solution:

\[
x = \frac{285}{37}, \quad y = -\frac{193}{37}, \quad z = \frac{44}{37}
\]

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

Here are 5 related questions to expand on this:
1. How can we verify solutions using substitution?
2. How do we handle systems where the variables are not aligned?
3. What other methods can be used to solve this system?
4. How does the value of \( z \) affect \(x\) and \(y\)?
5. Can these equations represent real-world problems?

**Tip:** When working with systems of equations, it's important to double-check each step to ensure accuracy, especially when substituting values!

Learn how to solve the system of linear equations 2x + y - z = 9, -x + 6y = -39, 5x + 7y = 2 with a detailed step-by-step solution. This problem involves solving a system of linear equations using substitution and simplification methods. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation