Question

Find all solutions of the given system of equations and briefly explain the steps you used to find your solution:

{3x - 2y = 4
9x - 6y = 12}

Answer 1

The system of equations has infinitely many solutions because both equations represent the same line. The solution is any point that lies on the line represented by the equation 3x - 2y = 4.

Step-by-step explanation:

To find all solutions of the given system of equations:

• 3x - 2y = 4
• 9x - 6y = 12

we can use the method of substitution or elimination. In this case, elimination might be more straightforward. Notice that the second equation is the first equation multiplied by 3. This suggests that both equations are actually the same line, therefore they will have infinitely many solutions.

Nevertheless, to solve the simultaneous equations, we proceed as follows:

1. First, we simplify the second equation by dividing it by 3, which gives us the equation identical to the first one: 3x - 2y = 4.
2. Since both equations are identical, they represent the same line, and thus any point on the line is a solution to the system.

The system does not have a single solution but instead has an infinite number of solutions represented by the equation of the line 3x - 2y = 4.