Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-15r + 12s = 24
30r – 24s = 48
did you notice the slope of the first line is 15/12 or 5/4
the slope of the second is 30/24 = 5/4
So the two lines are parallel.
Notice by multiplying the first by -2 we would get
30r - 24s = -48
since the constants are different, we have 2 different parallel line, which cannot intersect
So no solution.
To solve the system of equations using the elimination method, we need to eliminate one variable so that we can solve for the other variable. Here's how we can proceed:
Step 1: Multiply the first equation by 2 and the second equation by 1 so that the coefficients of 'r' in both equations will be equal:
2(-15r + 12s) = 2(24)
30r – 24s = 48
Simplifying these equations, we get:
-30r + 24s = 48
30r – 24s = 48
Step 2: Add the two equations together to eliminate the 'r' variable:
(-30r + 24s) + (30r – 24s) = 48 + 48
Simplifying, we get:
0 + 0 = 96
0 = 96
Step 3: We have obtained an equation that is always false (0 = 96), which means that the system has no solution. This occurs when the two equations represent parallel lines that do not intersect.
Therefore, the system of equations has no solution.