Find x, y, z, and w.

x	9	(2x − 1)	

y	7	4y
 = 

(2x − 5)	z	9	

5	(w + 1)	(3y + 5)


The problem you're presenting looks like a system of equations based on a matrix format. To solve for \( x \), \( y \), \( z \), and \( w \), I'll need to translate the grid into equations. From the matrix, I can identify several relationships between the variables. Let's break it down row by row:

### First row:
\[ x \quad 9 \quad (2x - 1) \]

### Second row:
\[ y \quad 7 \quad 4y \]

### Third row:
\[ (2x - 5) \quad z \quad 9 \]

### Fourth row:
\[ 5 \quad (w + 1) \quad (3y + 5) \]

These give us the following equations from the entries that appear to be related:

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

### Step-by-step solution:

#### Step 1: Solve for \( x \)
From the first equation:
\[ x = 9 \]

#### Step 2: Solve for \( y \)
From the second equation:
\[ y = 7 \]

#### Step 3: Solve for \( z \)
Now substitute \( x = 9 \) into the third equation:
\[
2x - 5 = z
\]
\[
2(9) - 5 = z
\]
\[
18 - 5 = z
\]
\[
z = 13
\]

#### Step 4: Solve for \( w \)
Now substitute \( y = 7 \) into the fourth equation:
\[
w + 1 = 3y + 5
\]
\[
w + 1 = 3(7) + 5
\]
\[
w + 1 = 21 + 5
\]
\[
w + 1 = 26
\]
\[
w = 25
\]

### Final answers:
- \( x = 9 \)
- \( y = 7 \)
- \( z = 13 \)
- \( w = 25 \)

Would you like further details or clarification on any of these steps?

Here are 5 related questions:
1. What are the steps for solving a system of linear equations in two variables?
2. Can matrix operations be used to solve a similar system?
3. How does substitution work in solving systems of equations?
4. What are the key methods for solving systems of equations?
5. How do you interpret a system of nonlinear equations?

**Tip**: Always check your solutions by plugging them back into the original equations to ensure correctness.

Find x, y, z, and w.
x  9  (2x − 1)
y  7  4y = (2x − 5) z  9
5  (w + 1)  (3y + 5)

Learn how to solve a system of linear equations involving x, y, z, and w with step-by-step explanations. This problem covers key algebraic concepts and substitution methods, suitable for students in Grades 9-10.

Math Problem Statement

y 7 4y

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation