Question 1090975
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You can use <a href="http://www.coolmath.com/algebra/14-determinants-cramers-rule/01-determinants-cramers-rule-2x2-01">Cramer's Rule</a> to solve this. Let's define the following

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<li>P = the matrix {{{(matrix(2,2,A,B,D,E))}}} (notice it's the left hand side coefficients)</li>
<li>Px = the matrix {{{(matrix(2,2,C,B,F,E))}}}. I started with matrix P and I've replaced the first column with C and F, both of which are the right hand side values</li>
<li>Py = the matrix {{{(matrix(2,2,A,C,D,F))}}}. I started with matrix P ann replaced the second column with C and F, both of which are the right hand side values</li>
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The notation det(P) is the determinant of matrix P. Using the <a href="http://www.purplemath.com/modules/determs.htm">two-by-two matrix determinant rule</a> we can say
{{{det(P) = A*E - B*D}}}
{{{det(Px) = C*E - F*B}}}
{{{det(Px) = A*F - C*D}}}


Then you divide the determinants to get x and y


{{{x = (det(Px))/(det(P)) = (C*E - F*B)/(A*E - B*D)}}}


{{{y = (det(Px))/(det(P)) = (A*F - C*D)/(A*E - B*D)}}}


If we knew the values of A,B,C,D,E, and F, then we could compute the actual numeric values of x and y. However, since we don't know those six variables, we just leave it as shown above. 


So the final answers are 
{{{x = (C*E - F*B)/(A*E - B*D)}}}


{{{y = (A*F - C*D)/(A*E - B*D)}}}
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