https://file.aiquickdraw.com/mathbot/file/17278144298041llhpivp.jpg

Let's solve problem 11 from the image, which presents the following system of equations:

\[
\begin{aligned}
0.25x - 0.05y &= 1 \\
0.25x + 0.1y &= 2.5
\end{aligned}
\]

We will solve this system using the **elimination method**.

### Step 1: Eliminate one variable
We want to eliminate one of the variables, so we can multiply both equations to align the coefficients of either \(x\) or \(y\). Let's eliminate \(x\) by subtracting the equations. Notice that the coefficients of \(x\) are already the same in both equations.

Start by subtracting the second equation from the first:

\[
(0.25x - 0.05y) - (0.25x + 0.1y) = 1 - 2.5
\]

Simplify:

\[
0.25x - 0.05y - 0.25x - 0.1y = -1.5
\]

This simplifies to:

\[
-0.15y = -1.5
\]

### Step 2: Solve for \(y\)
Now, solve for \(y\) by dividing both sides by \(-0.15\):

\[
y = \frac{-1.5}{-0.15} = 10
\]

So, \(y = 10\).

### Step 3: Substitute \(y = 10\) into one of the original equations
Now, substitute \(y = 10\) into one of the original equations, let's use the first equation:

\[
0.25x - 0.05(10) = 1
\]

Simplify:

\[
0.25x - 0.5 = 1
\]

Now solve for \(x\):

\[
0.25x = 1 + 0.5 = 1.5
\]

\[
x = \frac{1.5}{0.25} = 6
\]

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

\[
x = 6, \quad y = 10
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the elimination method differ if the coefficients of \(x\) were not the same in both equations?
2. Can we solve this system using substitution instead of elimination? How?
3. What happens if we multiply the entire system by 100 to eliminate decimals first?
4. How do you check if the solution is correct by substitution?
5. Can we solve this system using graphing, and what would the lines represent?

**Tip:** When solving systems with decimals, multiplying the entire equation by powers of 10 to eliminate decimals can make the arithmetic simpler!

Solve system of equations for 0.25x - 0.05y = 1 and 0.25x + 0.1y = 2.5 using elimination method.

Learn how to solve the system of linear equations 0.25x - 0.05y = 1 and 0.25x + 0.1y = 2.5 using the elimination method. Step-by-step guide provided, covering key algebraic concepts for students in Grades 8-10.

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