Question

Use system of equations


-7x -2y = -13

x - 2y = 11

Put steps in order:

Answer 1

bullet list the steps in order;

Answer 2

To solve the system of equations given by:

1) \(-7x - 2y = -13\)
2) \(x - 2y = 11\)

we can follow these steps:

### Step 1: Write the system of equations
\[
\begin{align*}
1. & \quad -7x - 2y = -13 \quad \text{(Equation 1)}\\
2. & \quad x - 2y = 11 \quad \text{(Equation 2)}
\end{align*}
\]

### Step 2: Solve one of the equations for one variable
Let's solve Equation 2 for \(x\):
\[
x = 11 + 2y
\]

### Step 3: Substitute the expression found in Step 2 into the other equation
Substitute \(x\) from Equation 2 into Equation 1:
\[
-7(11 + 2y) - 2y = -13
\]

### Step 4: Simplify and solve for \(y\)
Distributing \(-7\):
\[
-77 - 14y - 2y = -13
\]
Combine like terms:
\[
-77 - 16y = -13
\]
Add 77 to both sides:
\[
-16y = 64
\]
Divide by -16:
\[
y = -4
\]

### Step 5: Substitute back to find \(x\)
Now substitute \(y = -4\) back into Equation 2:
\[
x - 2(-4) = 11
\]
This simplifies to:
\[
x + 8 = 11
\]
Subtract 8 from both sides:
\[
x = 3
\]

### Step 6: Write the solution
The solution to the system of equations is:
\[
(x, y) = (3, -4)
\]

### Step 7: (Optional) Verify the solution
Substituting \(x = 3\) and \(y = -4\) into both original equations to confirm:

**For Equation 1:**
\[
-7(3) - 2(-4) = -21 + 8 = -13 \quad \text{(True)}
\]

**For Equation 2:**
\[
3 - 2(-4) = 3 + 8 = 11 \quad \text{(True)}
\]

Thus, the solution is verified. The answer is \((x, y) = (3, -4)\).

Answer 3

Sure! Here are the steps to solve the system of equations in bullet list format:

- **Step 1:** Write the system of equations:
- \( -7x - 2y = -13 \) (Equation 1)
- \( x - 2y = 11 \) (Equation 2)

- **Step 2:** Solve Equation 2 for \(x\):
- \( x = 11 + 2y \)

- **Step 3:** Substitute the expression for \(x\) into Equation 1:
- \( -7(11 + 2y) - 2y = -13 \)

- **Step 4:** Simplify and solve for \(y\):
- Distribute: \( -77 - 14y - 2y = -13 \)
- Combine like terms: \( -77 - 16y = -13 \)
- Add 77 to both sides: \( -16y = 64 \)
- Divide by -16: \( y = -4 \)

- **Step 5:** Substitute \(y = -4\) back into Equation 2 to find \(x\):
- \( x - 2(-4) = 11 \)
- Simplify: \( x + 8 = 11 \)
- Subtract 8 from both sides: \( x = 3 \)

- **Step 6:** Write the solution:
- The solution to the system of equations is \( (x, y) = (3, -4) \).

- **Step 7:** (Optional) Verify the solution by substituting back into the original equations.

This clear bullet list outlines the steps taken to solve the system of equations.