Solve the following system of equations: \(2x + 3y = 6\) and \(4x + 6y = 12\)
Answer
Step 3: The solutions to the system of equations are all pairs \((x, y)\) that satisfy this equation. That is, all pairs \((x, 2 - \frac{2}{3}x)\) for any real number \(x\).
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 \(y = 2 - \frac{2}{3}x\)
Step 3 ：Step 3: The solutions to the system of equations are all pairs \((x, y)\) that satisfy this equation. That is, all pairs \((x, 2 - \frac{2}{3}x)\) for any real number \(x\).
