What is the solution to this system of linear equations?

3x + 5y = 3
x + 4y = 8

		(-4, 3)
		(4, -3)
		(4, 4)
		(0, 2)
		(4, 3)


Let's solve the system of linear equations:

\[
3x + 5y = 3 \quad \text{(Equation 1)}
\]
\[
x + 4y = 8 \quad \text{(Equation 2)}
\]

### Step 1: Solve Equation 2 for \(x\):

\[
x = 8 - 4y
\]

### Step 2: Substitute \(x\) in Equation 1:

\[
3(8 - 4y) + 5y = 3
\]

### Step 3: Expand and solve for \(y\):

\[
24 - 12y + 5y = 3
\]
\[
24 - 7y = 3
\]
\[
-7y = 3 - 24
\]
\[
-7y = -21
\]
\[
y = \frac{-21}{-7} = 3
\]

### Step 4: Substitute \(y = 3\) back into Equation 2:

\[
x + 4(3) = 8
\]
\[
x + 12 = 8
\]
\[
x = 8 - 12 = -4
\]

### Solution:

The solution to the system of equations is \((-4, 3)\).

### Answer:
\((-4, 3)\) is the correct answer.

Would you like more details or have any questions? Here are five related questions to consider:

1. How do you solve a system of equations using substitution?
2. What is the elimination method for solving systems of linear equations?
3. How can graphing be used to solve a system of linear equations?
4. What are the possible outcomes when solving a system of linear equations?
5. How do you determine if a system of equations has no solution or infinitely many solutions?

**Tip:** Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of linear equations 3x + 5y = 3 and x + 4y = 8 with a step-by-step solution using the substitution method. Includes detailed steps for solving each equation and verifying the solution. 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