Let's solve the system of equations:

1. \( x + y = 200 \)
2. \( y - x = 50 \)

We can solve this system by adding the two equations to eliminate \( x \):

\[
(x + y) + (y - x) = 200 + 50
\]

This simplifies to:

\[
2y = 250
\]

So,

\[
y = \frac{250}{2} = 125
\]

Next, substitute \( y = 125 \) back into the first equation to find \( x \):

\[
x + 125 = 200
\]

\[
x = 200 - 125 = 75
\]

Therefore, the solutions are:

\[
x = 75, \quad y = 125
\]

Would you like more details or have any questions about this solution? 

Here are 5 questions you can ask next:
1. How do you solve a system of equations using the substitution method?
2. Can you explain the elimination method in more detail?
3. How would these solutions change if the system of equations were different?
4. What are some real-life applications of solving systems of equations?
5. How can I graphically represent the solution to this system of equations?

Tip: When solving systems of equations, always double-check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of equations x+y=200 and y-x=50 with a detailed step-by-step solution. This problem covers key algebraic concepts, including systems of linear equations and methods like substitution and elimination. Suitable for students in Grades 7-9.

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