write the solution to the simultaneous equations.

4x+y=0                 x-y=5

To solve the system of simultaneous equations:

\[
4x + y = 0 \tag{1}
\]
\[
x - y = 5 \tag{2}
\]

### Step 1: Solve one equation for one variable
From equation \((2)\), solve for \(x\):

\[
x = y + 5
\]

### Step 2: Substitute into the other equation
Substitute \(x = y + 5\) into equation \((1)\):

\[
4(y + 5) + y = 0
\]

Expand the expression:

\[
4y + 20 + y = 0
\]

Simplify:

\[
5y + 20 = 0
\]

### Step 3: Solve for \(y\)
Subtract 20 from both sides:

\[
5y = -20
\]

Now, divide by 5:

\[
y = -4
\]

### Step 4: Substitute \(y = -4\) back into the expression for \(x\)
Substitute \(y = -4\) into \(x = y + 5\):

\[
x = -4 + 5 = 1
\]

### Final solution:
\[
x = 1, \quad y = -4
\]

The solution to the simultaneous equations is:
\[
x = 1, \quad y = -4
\]

Would you like further details on this solution?

---

Here are 8 related questions for further exploration:
1. How would you solve the equations if they were nonlinear?
2. What happens if you change the second equation to \(x + y = 5\)?
3. How can simultaneous equations be solved graphically?
4. Can you solve the system using matrix methods like Cramer's Rule?
5. How would the solution change if \(4x + y = 2\)?
6. What is the determinant of the system if written as a matrix?
7. How can you verify the solution by substituting into both equations?
8. How can simultaneous equations be applied in real-world problems?

**Tip**: Always check your solutions by substituting the values of the variables back into the original equations.

Learn how to solve the system of simultaneous equations 4x + y = 0 and x - y = 5 with a detailed step-by-step solution. This problem covers key algebraic concepts of simultaneous equations and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation