Solve by Substitution 3x+6y=12 , x+2y=6

Problem

{[3*x+6*y=12],[x+2*y=6])

Solution

1. Isolate the variable x in the second equation by subtracting 2*y from both sides.

x=6−2*y

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

3*(6−2*y)+6*y=12

3. Distribute the constant 3 into the terms inside the parentheses.

18−6*y+6*y=12

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

18+0*y=12

5. Analyze the resulting statement.

18=12

6. Conclude that since the substitution leads to a false statement (18 = 12$), the system of equations is inconsistent and has no solution.

Final Answer

No solution

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