Solve by Substitution 2x+3y=6 , 4x+6y=24

Problem

{[2*x+3*y=6],[4*x+6*y=24])

Solution

1. Isolate a variable in the first equation. We will solve for x in 2*x+3*y=6

2*x=6−3*y

x=3−1.5*y

2. Substitute the expression for x into the second equation, 4*x+6*y=24

4*(3−1.5*y)+6*y=24

3. Distribute the constant into the parentheses.

12−6*y+6*y=24

4. Simplify the equation by combining like terms.

12+0*y=24

12=24

5. Interpret the result. Since the statement 12 = 24$ is a contradiction and is never true, the system of equations has no solution. The lines are parallel and do not intersect.

Final Answer

No Solution

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