find the soultion for -x+2y=13 and 5x+3y=13

To solve the system of linear equations:

\[
-x + 2y = 13 \quad (1)
\]
\[
5x + 3y = 13 \quad (2)
\]

We can use either substitution or elimination. Let's use substitution in this case:

### Step 1: Solve Equation (1) for \(x\).
From equation (1):
\[
-x = 13 - 2y \quad \Rightarrow \quad x = 2y - 13
\]

### Step 2: Substitute this expression for \(x\) in Equation (2).
Substitute \(x = 2y - 13\) into equation (2):
\[
5(2y - 13) + 3y = 13
\]
Expand the equation:
\[
10y - 65 + 3y = 13
\]
Simplify:
\[
13y - 65 = 13
\]
Add 65 to both sides:
\[
13y = 78
\]
Solve for \(y\):
\[
y = \frac{78}{13} = 6
\]

### Step 3: Substitute \(y = 6\) back into the expression for \(x\).
Now, substitute \(y = 6\) into the equation \(x = 2y - 13\):
\[
x = 2(6) - 13 = 12 - 13 = -1
\]

### Final Solution:
The solution to the system is:
\[
x = -1, \quad y = 6
\]

Would you like further details or have any questions about the solution? 

Here are 5 related questions for further practice:
1. Solve the system: \( 3x + 2y = 7 \) and \( 2x - y = 4 \).
2. Solve the system: \( 2x - y = 5 \) and \( -3x + 4y = -6 \).
3. What is the graphical interpretation of the solution \(x = -1\), \(y = 6\)?
4. Use the elimination method to solve: \(4x + 3y = 18\) and \(6x - 5y = 12\).
5. Solve a 3-variable system: \(x + y + z = 10\), \(2x - y + z = 5\), and \(3x + 2y - z = 15\).

**Tip:** Always double-check your solution by substituting the values of \(x\) and \(y\) back into both original equations.

find the solution for -x + 2y = 13 and 5x + 3y = 13

Learn how to solve the system of linear equations -x + 2y = 13 and 5x + 3y = 13 using the substitution method. This step-by-step guide covers key algebraic concepts 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