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

Problem

{[x+2*y=2],[−x−2*y+2=0])

Solution

1. Isolate a variable in the first equation. We can solve for x by subtracting 2*y from both sides.

x=2−2*y

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

−(2−2*y)−2*y+2=0

3. Distribute the negative sign through the parentheses.

−2+2*y−2*y+2=0

4. Combine like terms on the left side of the equation.

0=0

5. Interpret the result. Since the substitution leads to a statement that is always true (0 = 0$), the two equations represent the same line. This means there are infinitely many solutions along that line.

Final Answer

Infinitely many solutions

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