Solve by Substitution 2x+y=2 , 8x+4y=8

Problem

{[2*x+y=2],[8*x+4*y=8])

Solution

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

y=2−2*x

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

8*x+4*(2−2*x)=8

3. Distribute the constant into the parentheses.

8*x+8−8*x=8

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

8=8

5. Interpret the result. Since the statement 8 = 8$ is always true and the variables have canceled out, the two equations represent the same line. This means there are infinitely many solutions.

Final Answer

Infinitely many solutions

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