SOLUTION: How do you solve 4x-4y=8, 8x-8y=24 using Cramer's Rule?

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Question 865696: How do you solve 4x-4y=8, 8x-8y=24 using Cramer's Rule?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables



system%284%2Ax%2B-4%2Ay=8%2C8%2Ax%2B-8%2Ay=24%29



First let A=%28matrix%282%2C2%2C4%2C-4%2C8%2C-8%29%29. This is the matrix formed by the coefficients of the given system of equations.


Take note that the right hand values of the system are 8 and 24 which are highlighted here:
system%284%2Ax%2B-4%2Ay=highlight%288%29%2C8%2Ax%2B-8%2Ay=highlight%2824%29%29



These values are important as they will be used to replace the columns of the matrix A.




Now let's calculate the the determinant of the matrix A to get abs%28A%29=%284%29%28-8%29-%28-4%29%288%29=0. Remember that the determinant of the 2x2 matrix A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 is abs%28A%29=ad-bc. If you need help with calculating the determinant of any two by two matrices, then check out this solver.



Notation note: abs%28A%29 denotes the determinant of the matrix A.



Since the determinant of matrix A is zero, this means that we cannot use Cramer's Rule. Why? Remember that each solution 'x' and 'y' are found by dividing by the determinant of A. If that determinant is zero, then you'll be dividing by zero, which is undefined. So that means you have to use an alternate method to find the solution.