Solve by Substitution x+4y=4 , -x-4y+4=0

Problem

{[x+4*y=4],[−x−4*y+4=0])

Solution

1. Isolate a variable in the first equation. We can solve for x by subtracting 4*y from both sides.

x=4−4*y

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

−(4−4*y)−4*y+4=0

3. Distribute the negative sign through the parentheses.

−4+4*y−4*y+4=0

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

0=0

5. Interpret the result. Since the substitution leads to a true statement that does not depend on the variables, the two equations represent the same line. This means there are infinitely many solutions along the line x+4*y=4

Final Answer

Infinitely many solutions

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