Solve by Substitution x+y=2 , 2x+2y=-6

Problem

{[x+y=2],[2*x+2*y=−6])

Solution

1. Isolate a variable in the first equation. We can subtract y from both sides to solve for x

x=2−y

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

2*(2−y)+2*y=−6

3. Distribute the constant into the parentheses.

4−2*y+2*y=−6

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

4+0=−6

5. Analyze the resulting statement. The equation simplifies to a false statement.

4=−6

6. Conclude that since the variables were eliminated and the resulting numerical statement is false, the system of equations is inconsistent.

Final Answer

No solution

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