Answer:
(x, y) = (4, 6)
Step-by-step explanation:
The fractions can be eliminated from the equations by multiplying both of them by 12:
9x -10y = -24
-x +2y = 8
Cramer's Rule solves these using three determinants. One is of the matrix of coefficients. One is of that matrix where x-coefficients are replaced by the constants. The remaining one is of the coefficient matrix where y-coefficients are replaced by the constants.
If we call the determinants d1, d2, d3, then the solutions are ...
x = d2/d1
y = d3/d1
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[tex]d1=\left|\begin{array}{cc}9&-10\\-1&2\end{array}\right|=18-10=8\\\\d2=\left|\begin{array}{cc}-24&-10\\8&2\end{array}\right|=-48+80=32\\\\d3=\left|\begin{array}{cc}9&-24\\-1&8\end{array}\right|=72-24=48\\\\x=\dfrac{32}{8}=4\\\\y=\dfrac{48}{8}=6[/tex]
The solution is (x, y) = (4, 6).
