https://file.aiquickdraw.com/mathbot/file/1729447959913wlxnnj7o.jpg

The system of equations provided is:

\[
1. \ 4x + 3y = 8
\]
\[
2. \ 4x + 6y = 20
\]

### Step 1: Eliminate one variable
We can eliminate \( x \) by subtracting the first equation from the second.

\[
(4x + 6y) - (4x + 3y) = 20 - 8
\]

This simplifies to:

\[
6y - 3y = 12 \quad \Rightarrow \quad 3y = 12
\]

Solve for \( y \):

\[
y = \frac{12}{3} = 4
\]

### Step 2: Substitute \( y = 4 \) into one of the original equations
Substitute \( y = 4 \) into the first equation \( 4x + 3y = 8 \):

\[
4x + 3(4) = 8
\]

This simplifies to:

\[
4x + 12 = 8 \quad \Rightarrow \quad 4x = 8 - 12 \quad \Rightarrow \quad 4x = -4
\]

Solve for \( x \):

\[
x = \frac{-4}{4} = -1
\]

### Final Solution:
The solution to the system of equations is:
\[
x = -1, \quad y = 4
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What happens if we solve this system graphically? What do the lines represent?
2. How do you solve a system of equations using substitution instead of elimination?
3. What would happen if both equations represented the same line?
4. How can we solve a system of three variables using elimination?
5. What are the possible outcomes when solving a system of linear equations (one solution, no solution, infinitely many solutions)?

**Tip:** Always check your solution by plugging the values of \( x \) and \( y \) back into both original equations to ensure they satisfy both!

Solve the following system of equations: 4x + 3y = 8, 4x + 6y = 20

Learn how to solve the system of linear equations 4x + 3y = 8 and 4x + 6y = 20 using the elimination method. This step-by-step guide simplifies 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