Solve by Substitution x-y=2 , x-y=0

Problem

{[x−y=2],[x−y=0])

Solution

1. Solve the first equation for x to express it in terms of y

x−y=2

x=y+2

2. Substitute the expression for x into the second equation.

x−y=0

(y+2)−y=0

3. Simplify the resulting equation by combining like terms.

y−y+2=0

2=0

4. Interpret the result. Since the substitution leads to a false statement (2 = 0$), the system of equations has no solution. This indicates that the two lines are parallel and never intersect.

Final Answer

No solution

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