0,5x - 1,4 y = 33 dan 0 dan 35x - 0,12 y = 5,9 adalah (x,y). Maka nilai x-y=

We are given two linear equations and asked to solve for \( x - y \). The equations are:

1. \( 0.5x - 1.4y = 33 \)
2. \( 35x - 0.12y = 5.9 \)

We will solve this system using either substitution or elimination. Let's proceed step by step.

### Step 1: Eliminate decimals by multiplying both equations by appropriate factors
To simplify the equations, multiply both equations to remove the decimals.

Multiply the first equation by 10:
\[
5x - 14y = 330
\]

Multiply the second equation by 100:
\[
3500x - 12y = 590
\]

### Step 2: Use elimination method
To eliminate \( y \), let's multiply the first equation by 6 and the second by 7 to make the coefficients of \( y \) the same.

- Multiply the first equation \( 5x - 14y = 330 \) by 6:
\[
30x - 84y = 1980
\]

- Multiply the second equation \( 3500x - 12y = 590 \) by 7:
\[
24500x - 84y = 4130
\]

### Step 3: Subtract the first equation from the second
Now subtract the first equation from the second:

\[
(24500x - 84y) - (30x - 84y) = 4130 - 1980
\]

Simplifying this gives:
\[
24470x = 2150
\]

### Step 4: Solve for \( x \)
\[
x = \frac{2150}{24470} \approx 0.0879
\]

### Step 5: Substitute \( x \) into one of the original equations
Now substitute \( x = 0.0879 \) into the first equation:
\[
5(0.0879) - 14y = 330
\]

Simplify:
\[
0.4395 - 14y = 330
\]

Solve for \( y \):
\[
-14y = 330 - 0.4395
\]
\[
-14y = 329.5605
\]
\[
y = \frac{329.5605}{-14} \approx -23.54
\]

### Step 6: Find \( x - y \)
\[
x - y = 0.0879 - (-23.54) = 0.0879 + 23.54 = 23.63
\]

Thus, the value of \( x - y \) is approximately \( \boxed{23.63} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve a system of linear equations using substitution?
2. What are the key differences between substitution and elimination methods?
3. Can you explain how to handle decimals in linear equations?
4. What is the geometric interpretation of solving two linear equations?
5. How can linear equations be applied to real-world problems?

**Tip:** When solving systems of equations, eliminating decimals early can make calculations simpler and reduce errors.

Learn how to solve the system of linear equations 0.5x - 1.4y = 33 and 35x - 0.12y = 5.9 using the elimination method. This step-by-step solution includes tips on handling decimals and finding x - y. Ideal for students in Grades 10-12.

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