Period+6+-+Cramer's+Rule+2x2

Justin, Eun & Ali
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 * Cramer's Rule involves multiplying and subtracting the coefficients of a particular system because you need to find the determinants.
 * Rather than solving systems using substitution or elimination, Cramer's Rule can be applied.
 * To find out why this is read as a 2x2 system, click here.
 * Just know the formula to find the determinant because you will need it. It goes as follows:




 * Cramer's Rule for 2x2 can be identified by the following:




 * Three different determinants are used to find **x** and **y** (sometimes seen as **Dx** and **Dy**).
 * The elements of D, which is the determinant in both denominators, are the coefficients of variables in the system: coefficients of x in the first column and of y in the second column.
 * *Know that if D is 0, Cramer's Rule cannot be applied. If D=0, the system is either considered consistent or dependent, so another method must be used to solve the system.
 * Dx is the determinant in the numerator of x. It can be found by replacing the x-coefficients, [[image:http://www.okc.cc.ok.us/maustin/Cramers_Rule/Image999.gif width="66" height="22" align="BOTTOM"]], in D with the constants from the right sides of the equations, [[image:http://www.okc.cc.ok.us/maustin/Cramers_Rule/Image1000.gif width="64" height="22" align="BOTTOM"]].
 * Dy is the determinant in the numerator of y. It can be found by replacing the y-coefficients,[[image:http://www.okc.cc.ok.us/maustin/Cramers_Rule/Image1003.gif width="64" height="22" align="BOTTOM"]], in D with the constants from the right side of the equation, [[image:http://www.okc.cc.ok.us/maustin/Cramers_Rule/Image1000.gif width="64" height="22" align="BOTTOM"]].



__Example__: Use Cramer's Rule to solve a system of equations
System:
 * 5x - 4y = 2 **
 * 6x - 5y = 1 **


 * Start by setting up three equations to evaluate the determinants (D, Dx, Dy):






 * Solve each determinant:






 * Find the result (x,y) by dividing:
 * x = (Dx)/(D) and y = (Dy)/(D)
 * Solution is the ordered pair: (6, 7)

More Practice Problems:
3x+5y=33 4x-3y=15
 * solution: (6,3)

2x+3y=11 4y-x=0
 * solution (4,1)

Youtube Video:
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**Sources**:
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