5. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
9x + 6y = 60
-27x Ð 18y = -180
Here's where I am at now:
9x(3) + 6y(3) = 60
27x +18y + 60
27 x + 18y = 60
-27x -18y = 180
Im stuck here because the x and y appear to cancel.
Any suggestions or assistance anyone?
it has no solution because 0 doesnt equal 180
the lines never meet
To solve the given system of equations using the elimination method, we can multiply one or both equations by appropriate numbers so that when added or subtracted, either the x-coefficients or y-coefficients will cancel out.
Let's start with the equations:
1) 9x + 6y = 60
2) -27x - 18y = -180
To eliminate the x-coefficients, we can multiply equation 1 by 3, and equation 2 by -1. Thus, the equations become:
3) 27x + 18y = 180
4) 27x + 18y = 180
Notice that equations 3 and 4 are identical. This means that the system of equations represents the same line, and therefore, there are infinitely many solutions.
The elimination method is not applicable when the coefficients of x and y in both equations are proportional to each other, resulting in identical equations like we have here. In such cases, either the two equations represent the same line (infinitely many solutions) or parallel lines (no solution).
Thus, the given system of equations has infinitely many solutions.