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

Problem

{[2*x+y=6],[6*x=−3*y+12])

Solution

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

y=6−2*x

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

6*x=−3*(6−2*x)+12

3. Distribute the −3 through the parentheses on the right side.

6*x=−18+6*x+12

4. Simplify the right side by combining the constant terms.

6*x=6*x−6

5. Subtract 6*x from both sides to isolate the constants.

0=−6

6. Interpret the result. Since 0 = -6$ is a false statement, the system of equations is inconsistent and has no solution.

Final Answer

No solution

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