Question

solve the system.
5 + x = y
y - 5 = x
solution:
the solution is (0, 5)
the solution is (5, 0)
there is no solution.
there are infinitely many solutions.

Explanation:

Step1: Analyze the system of equations

We have the system:

• Equation 1: \( y = 5 + x \)
• Equation 2: \( x = y - 5 \)

Let's rewrite Equation 2 to see its relation to Equation 1. If we add 5 to both sides of Equation 2, we get \( y = x + 5 \), which is exactly the same as Equation 1.

Step2: Determine the number of solutions

When two equations in a system are identical (they represent the same line), every point on that line is a solution to the system. So, there are infinitely many solutions because the two equations are dependent (they are the same equation, just written in different forms).

Answer:

There are infinitely many solutions.