Process of eliminiation method ? Is there a solution, infinity or no solution. I don't get it. Can anyone help me?
3r - 5s = -27
5r + 3s = 23
The process of elimination is a method used to solve a system of equations by eliminating one variable at a time. Let's go step by step to solve the given system of equations.
Given system of equations:
3r - 5s = -27 ... (1)
5r + 3s = 23 ... (2)
To eliminate one variable, we need to manipulate one or both equations so that when we add or subtract them, one variable will be eliminated. In this case, we can eliminate the variable "s" by multiplying equation (1) by 3 and equation (2) by 5, then adding them together:
(3 * (3r - 5s)) + (5 * (5r + 3s)) = (3 * -27) + (5 * 23)
9r - 15s + 25r + 15s = -81 + 115
34r = 34
r = 34/34
r = 1
Now that we have found the value of "r," we can substitute it back into one of the original equations and solve for "s." Let's use equation (1):
3(1) - 5s = -27
3 - 5s = -27
-5s = -27 - 3
-5s = -30
s = (-30)/(-5)
s = 6
So, the solution to the system of equations is:
r = 1
s = 6
Therefore, there is a unique solution for the given system of equations.