You are given a system of linear equations:

1. \( 3x + 2y = 0 \)
2. \( y = 2x - 1 \)

Let's solve this system by substitution since \( y = 2x - 1 \) is already isolated.

### Step 1: Substitute \( y = 2x - 1 \) into the first equation.
Substitute \( 2x - 1 \) for \( y \) in the equation \( 3x + 2y = 0 \):

\[
3x + 2(2x - 1) = 0
\]

### Step 2: Simplify the equation.
Expand the terms inside the parentheses:

\[
3x + 4x - 2 = 0
\]

Combine like terms:

\[
7x - 2 = 0
\]

### Step 3: Solve for \( x \).
Add 2 to both sides:

\[
7x = 2
\]

Now, divide by 7:

\[
x = \frac{2}{7}
\]

### Step 4: Solve for \( y \).
Now that we have \( x = \frac{2}{7} \), substitute this value into the second equation \( y = 2x - 1 \):

\[
y = 2\left(\frac{2}{7}\right) - 1 = \frac{4}{7} - 1
\]

Convert 1 to a fraction:

\[
y = \frac{4}{7} - \frac{7}{7} = \frac{-3}{7}
\]

### Final Solution:
The solution to the system of equations is:
\[
x = \frac{2}{7}, \quad y = \frac{-3}{7}
\]

Would you like further details or have any questions?

Here are 5 related questions for you to explore:
1. How can you graphically represent the system of equations?
2. What happens if the equations represent parallel lines?
3. Can this method be used to solve non-linear systems?
4. How does the substitution method compare to the elimination method?
5. What would change if the second equation was \( y = 3x - 1 \)?

**Tip:** When solving systems of equations, always check if substitution or elimination is more straightforward based on how the equations are given.

Learn how to solve the system of linear equations 3x + 2y = 0 and y = 2x - 1 using the substitution method. This problem explores key algebraic concepts and provides a step-by-step solution suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation