Solve the system of linear equation {2x+y=10,-x-2y=15

To solve the system of linear equations:

\[
\begin{aligned}
1) \ \ 2x + y &= 10 \\
2) \ \ -x - 2y &= 15
\end{aligned}
\]

### Step 1: Solve one equation for one variable
Let's solve equation \( (1) \) for \( y \):

\[
2x + y = 10 \implies y = 10 - 2x
\]

### Step 2: Substitute into the other equation
Substitute \( y = 10 - 2x \) into equation \( (2) \):

\[
-x - 2(10 - 2x) = 15
\]

Now simplify:

\[
-x - 20 + 4x = 15
\]
\[
3x - 20 = 15
\]

### Step 3: Solve for \( x \)
Add 20 to both sides:

\[
3x = 35
\]

Now, divide by 3:

\[
x = \frac{35}{3}
\]

### Step 4: Substitute \( x \) back into the equation for \( y \)
Substitute \( x = \frac{35}{3} \) into \( y = 10 - 2x \):

\[
y = 10 - 2\left(\frac{35}{3}\right)
\]
\[
y = 10 - \frac{70}{3}
\]
\[
y = \frac{30}{3} - \frac{70}{3} = \frac{-40}{3}
\]

### Final Solution
The solution to the system is:

\[
x = \frac{35}{3}, \quad y = \frac{-40}{3}
\]

Would you like more details or have any questions?

---

Here are 5 related questions:
1. How can substitution be used for more complex systems of equations?
2. What is the elimination method, and how could it be applied here?
3. How would you interpret these results geometrically?
4. How do you handle systems of equations with no solutions?
5. What is the matrix method for solving systems of linear equations?

**Tip:** Always double-check your substitution steps to avoid small arithmetic errors that can lead to incorrect results.

Solve the system of linear equations {2x + y = 10, -x - 2y = 15}

Learn how to solve the system of linear equations 2x + y = 10 and -x - 2y = 15 using the substitution method. This step-by-step solution is ideal for students in Grades 9-11, covering key algebraic concepts and linear equation theorems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation