https://file.aiquickdraw.com/mathbot/file/1733563029444fph6tedd.jpg

The given system of equations is:

\[
\begin{cases}
x + y = 7 \\
y - x = -1
\end{cases}
\]

Let's solve this system step by step.

---

### Step 1: Solve one equation for one variable
From the first equation:
\[
x + y = 7 \implies y = 7 - x
\]

---

### Step 2: Substitute into the second equation
Substitute \( y = 7 - x \) into the second equation \( y - x = -1 \):
\[
(7 - x) - x = -1
\]
Simplify:
\[
7 - 2x = -1
\]
\[
-2x = -1 - 7
\]
\[
-2x = -8 \implies x = 4
\]

---

### Step 3: Substitute \( x = 4 \) back into \( y = 7 - x \)
\[
y = 7 - 4 = 3
\]

---

### Final Solution:
\[
x = 4, \, y = 3
\]

---

Would you like further explanation or a graph of the solution?  

Here are some related questions to deepen understanding:
1. What is the graphical representation of this system of equations?
2. Can this system be solved using matrix methods?
3. How do we confirm the solution satisfies both equations?
4. What would happen if the equations represented parallel lines?
5. How is substitution different from elimination in solving such systems?

**Tip**: Always substitute your solution back into both equations to verify its correctness!

Solve the given system of linear equations: x + y = 7 and y - x = -1.

Learn how to solve a system of linear equations using substitution. This example demonstrates solving x + y = 7 and y - x = -1 step by step. Ideal for students in Grades 8-10 learning about algebraic methods.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation