We are given a system of two linear equations:

1. \( 4x + 5y = 2 \)
2. \( -2x - y = -3 \)

We can solve this system using either substitution or elimination. Let's use the elimination method.

### Step 1: Eliminate one variable

Multiply the second equation by 2 to make the coefficients of \( x \) in both equations opposites:
\[
2(-2x - y) = 2(-3)
\]
This simplifies to:
\[
-4x - 2y = -6
\]

Now we have the system:
1. \( 4x + 5y = 2 \)
2. \( -4x - 2y = -6 \)

### Step 2: Add the two equations

\[
(4x + 5y) + (-4x - 2y) = 2 + (-6)
\]
This simplifies to:
\[
3y = -4
\]

### Step 3: Solve for \( y \)

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

### Step 4: Substitute \( y = \frac{-4}{3} \) into one of the original equations

We'll use the first equation \( 4x + 5y = 2 \):
\[
4x + 5\left(\frac{-4}{3}\right) = 2
\]
\[
4x - \frac{20}{3} = 2
\]
Multiply through by 3 to eliminate the fraction:
\[
12x - 20 = 6
\]
\[
12x = 26
\]
\[
x = \frac{26}{12} = \frac{13}{6}
\]

### Final Solution:
\[
x = \frac{13}{6}, \quad y = \frac{-4}{3}
\]

Let me know if you need further details or have any questions!

### Related Questions:
1. How do you verify the solution of a system of linear equations?
2. What are the different methods for solving a system of linear equations?
3. Can every system of linear equations be solved by elimination?
4. How can you solve a system of linear equations graphically?
5. What does it mean if a system of equations has no solution?

### Tip:
When using elimination, multiplying to align coefficients is key for eliminating variables efficiently!

Learn how to solve the system of linear equations 4x + 5y = 2 and -2x - y = -3 using the elimination method. This step-by-step guide covers key algebraic concepts and is 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