Solve the system of equations by any method.

 

5x+9y=17
x+2y=4

To solve the system of equations:

\[
5x + 9y = 17
\]
\[
x + 2y = 4
\]

we can use the **substitution method** or **elimination method**. I'll proceed with the substitution method here.

### Step 1: Solve for \( x \) in the second equation
From the equation:
\[
x + 2y = 4
\]
we can isolate \( x \):
\[
x = 4 - 2y
\]

### Step 2: Substitute \( x = 4 - 2y \) into the first equation
Substitute this expression for \( x \) in the first equation:
\[
5(4 - 2y) + 9y = 17
\]

Expanding and simplifying:
\[
20 - 10y + 9y = 17
\]
\[
20 - y = 17
\]
\[
-y = -3
\]
\[
y = 3
\]

### Step 3: Substitute \( y = 3 \) back into the expression for \( x \)
Now, substitute \( y = 3 \) into \( x = 4 - 2y \):
\[
x = 4 - 2(3)
\]
\[
x = 4 - 6
\]
\[
x = -2
\]

### Solution
The solution to the system is:
\[
x = -2, \quad y = 3
\]

---

Would you like further details on this solution, or do you have any questions?

Here are some related questions to consider:
1. How do you apply the elimination method for this system?
2. What are the differences between substitution and elimination methods?
3. How can you verify that a solution is correct for a system of equations?
4. What does it mean if a system has no solution or infinitely many solutions?
5. How would graphing the equations help in understanding the solution?

**Tip:** Always substitute the values back into the original equations to confirm that your solution is correct.

Solve the system of equations by any method.

5x + 9y = 17
x + 2y = 4

Learn how to solve the system of linear equations 5x + 9y = 17 and x + 2y = 4 using the substitution method. This problem covers key algebraic concepts suitable for Grades 8-10, including substitution and elimination methods in systems of linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation