sovle for system of elimination, 3x+5y = 13, 2x+y=4

We are solving the system of linear equations using the **elimination method**:

\[
\text{1) } 3x + 5y = 13
\]
\[
\text{2) } 2x + y = 4
\]

### Step 1: Make the coefficients of one variable the same
We will eliminate \(y\) by making the coefficients of \(y\) in both equations equal. To do that, multiply the second equation by 5:

\[
5(2x + y) = 5(4)
\]
\[
\text{This gives: } 10x + 5y = 20 \quad \text{(Equation 3)}
\]

Now the system is:
\[
\text{1) } 3x + 5y = 13
\]
\[
\text{3) } 10x + 5y = 20
\]

### Step 2: Subtract the equations
Subtract equation 1 from equation 3 to eliminate \(y\):

\[
(10x + 5y) - (3x + 5y) = 20 - 13
\]
\[
7x = 7
\]

### Step 3: Solve for \(x\)
\[
x = \frac{7}{7} = 1
\]

### Step 4: Substitute \(x = 1\) into one of the original equations
Substitute \(x = 1\) into equation 2:
\[
2(1) + y = 4
\]
\[
2 + y = 4
\]
\[
y = 4 - 2 = 2
\]

### Final Solution:
\[
x = 1, \quad y = 2
\]

The solution to the system of equations is \(x = 1\) and \(y = 2\).

Would you like further details or have any questions?

### Related questions:
1. How does the elimination method differ from the substitution method?
2. What happens if both variables have the same coefficient initially?
3. How can you solve a system where the equations are dependent or inconsistent?
4. Can the elimination method be applied to more than two equations?
5. What if both variables are eliminated and you get a false statement?

**Tip:** Always check your solution by substituting the values back into the original equations to verify correctness.

solve for system of elimination, 3x+5y = 13, 2x+y=4

Learn how to solve a system of linear equations using the elimination method. This example covers the equations 3x + 5y = 13 and 2x + y = 4 with a detailed step-by-step solution. This problem is suitable for students in Grades 8-10 and focuses on algebraic techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation