Cramer's Rule and a System of Two EquationsDate: 12/27/2003 at 17:40:43 From: Brittany Subject: using Cramer's Rule Find x and y using Cramer's Rule: 2x - 6y = 12 -4x + 3y = 7 Date: 12/27/2003 at 19:38:01 From: Doctor Rob Subject: Re: using Cramer's Rule Thanks for writing to Ask Dr. Math, Brittany! Cramer's Rule says that in such situations, x and y can be written as the quotient of two determinants. The denominator is the same for both x and y: it's two-by-two and contains the coefficients of x and y from the two equations as entries, one row for each equation and one column for each variable x and y: 2x - 6y --> | 2 -6| -4x + 3y --> |-4 3| The numerator for x is found by replacing the column containing the coefficients of x by a column containing the constants from the right side of the equations: 2x - 6y = 12 --> |12 -6| -4x + 3y = 7 --> | 7 3| The numerator for y is found by replacing the column containing the coefficients of y by a column containing the constants from the right side of the equations: 2x - 6y = 12 --> | 2 12| -4x + 3y = 7 --> |-4 7| Compute these determinant values, and then take the quotients indicated above, and you'll have the solution values of x and y: |12 -6| | 7 3| (12)(3) - (7)(-6) 36 - (-42) 78 13 x = --------- = ----------------- = ---------- = ---- = -- | 2 -6| (2)(3) - (-4)(-6) 6 - 24 -18 -3 |-4 3| | 2 12| |-4 7| y = --------- = ? | 2 -6| |-4 3| Feel free to write again if I can help further. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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