direction state : solve each system by addition. if a unique solution does not exist, state whether the system is consistent or dependent.
NOw the problem looks like this:
2x+3y=1
5x+3y=16
the answer that I got was this:
for variable x = 5
y = -3
which is the same as (5,-3)
now how do i determine if this system of solution is consistent or dependent?
thanks to everyone who looked into it but luckally i figured it out.
To determine if the system of equations is consistent or dependent, you can check if the system has a unique solution or infinitely many solutions.
In this case, the system is consistent because it has a unique solution, which is (5, -3).
To explain how to get this answer using the method of addition, let's go through the process step-by-step:
Step 1: Write the system of equations:
2x + 3y = 1 (Equation 1)
5x + 3y = 16 (Equation 2)
Step 2: Choose one variable to eliminate. In this case, let's eliminate the y variable. To do that, we can multiply Equation 1 by 3 and Equation 2 by -3 so that the coefficients of y will have opposite signs:
3(2x + 3y) = 3(1) --> 6x + 9y = 3 (Equation 3)
(-3)(5x + 3y) = (-3)(16) --> -15x - 9y = -48 (Equation 4)
Step 3: Add Equation 3 and Equation 4 to eliminate the y variable:
(6x + 9y) + (-15x - 9y) = 3 + (-48)
x = -45
Step 4: Substitute the value of x back into one of the original equations to solve for the other variable. Let's use Equation 1:
2(-45) + 3y = 1
-90 + 3y = 1
3y = 91
y = 91/3
y = -3
Therefore, the solution to the system of equations is x = -45 and y = -3, or (x,y) = (5, -3).
Since there is a unique solution, the system of equations is consistent.