https://file.aiquickdraw.com/mathbot/file/17273738748770muuzv0t.jpg

The image contains a system of simultaneous equations involving the variables \(x\), \(y\), and \(w\). The equations are:

\[
\begin{aligned}
1. & \quad x + 2y = 143 \\
2. & \quad y + 3w = -74 \\
3. & \quad 4x + 5w = 4 \\
\end{aligned}
\]

### Let's solve this system of equations.

1. From the first equation, we can express \(x\) in terms of \(y\):
   \[
   x = 143 - 2y
   \]

2. Now substitute this expression for \(x\) into the third equation:
   \[
   4(143 - 2y) + 5w = 4
   \]
   Simplifying this:
   \[
   572 - 8y + 5w = 4
   \]
   \[
   -8y + 5w = 4 - 572
   \]
   \[
   -8y + 5w = -568
   \]
   \[
   8y - 5w = 568 \quad \text{(Equation 4)}
   \]

3. Now we have the system:
   \[
   \begin{aligned}
   & y + 3w = -74 \quad \text{(Equation 2)} \\
   & 8y - 5w = 568 \quad \text{(Equation 4)}
   \end{aligned}
   \]

We will solve this system for \(y\) and \(w\). I'll calculate the solution now.The solution to the system for \(y\) and \(w\) is:

\[
y = 46 \quad \text{and} \quad w = -40
\]

4. Now, using the value of \(y = 46\) in the equation for \(x\):
   \[
   x = 143 - 2(46) = 143 - 92 = 51
   \]

### Final solution:
\[
x = 51, \quad y = 46, \quad w = -40
\]

Would you like a more detailed explanation, or do you have any other questions?

---

Here are some related questions for deeper exploration:
1. How do you solve systems of equations using substitution?
2. What is the elimination method in solving systems of equations?
3. Can systems of linear equations always be solved?
4. How does changing the coefficients affect the solutions?
5. What methods are used to solve systems of nonlinear equations?

**Tip:** When solving systems of equations, substitution is efficient when one equation can easily be rearranged for a single variable.

Solve the system of simultaneous equations: x + 2y = 143, y + 3w = -74, 4x + 5w = 4.

Learn how to solve the system of linear equations x + 2y = 143, y + 3w = -74, and 4x + 5w = 4 using the substitution method. This detailed step-by-step solution covers key algebraic concepts, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation