Problem

Solve the following system of equations: 2x+3y=6 and 4x+6y=12

Answer

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Answer

Step 3: The solutions to the system of equations are all pairs (x,y) that satisfy this equation. That is, all pairs (x,2−23x) for any real number x.

Steps

Step 1 ：Step 1: Notice that the second equation is just the first equation multiplied by 2. This means that the system of equations is dependent, and there are infinitely many solutions.

Step 2 ：Step 2: To find these solutions, we can solve the first equation for y in terms of x: 3y=6−2x or y=2−23x

Step 3 ：Step 3: The solutions to the system of equations are all pairs (x,y) that satisfy this equation. That is, all pairs (x,2−23x) for any real number x.

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