Participation Activity \#5 This is similar to Try It \#7 in the OpenStax text. Solve the following system of equations in two variables. \[ y-3 x=5 \] \[ -3 y+9 x=-15 \]

To solve the system of equations given, we can start by rearranging the first equation to express \( y \) in terms of \( x \): 1. From the first equation \( y - 3x = 5 \): \[ y = 3x + 5 \] 2. Now, substitute \( y \) into the second equation \( -3y + 9x = -15 \): \[ -3(3x + 5) + 9x = -15 \] 3. Simplifying this: \[ -9x - 15 + 9x = -15 \] \[ -15 = -15 \] Since this statement is true for all values of \( x \), the system has infinitely many solutions. We can conclude that the two equations actually represent the same line. Thus, any point of the form \( (x, 3x + 5) \) is a solution. For example, if \( x = 0 \), then \( y = 5 \), giving us the solution point \( (0, 5) \). So, there are infinitely many solutions!