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

Problem

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

Solution

1. Clear the fractions in the first equation by multiplying every term by the least common multiple of the denominators, which is 6

x/2*(6)+y/3*(6)=4*(6)

3*x+2*y=24

2. Clear the fractions in the second equation by multiplying every term by the least common multiple of the denominators, which is 12

x/4*(12)+y/6*(12)=2*(12)

3*x+2*y=24

3. Compare the equations and observe that both equations simplify to the exact same linear expression.

3*x+2*y=24

3*x+2*y=24

4. Solve for one variable in terms of the other to express the general solution, since the system is dependent.

2*y=24−3*x

y=12−3/2*x

5. Identify the solution type as having infinitely many solutions because the two lines are coincident.

Final Answer

Infinitely many solutions of the form *(x,12−3/2*x)

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