Solve for x_1
x_{1}=-\frac{9-2x_{2}}{x_{2}-7}
x_{2}\neq 7
Solve for x_2
x_{2}=-\frac{9-7x_{1}}{x_{1}-2}
x_{1}\neq 2
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-7x_{1}+x_{1}x_{2}=-9+2x_{2}
Add 2x_{2} to both sides.
\left(-7+x_{2}\right)x_{1}=-9+2x_{2}
Combine all terms containing x_{1}.
\left(x_{2}-7\right)x_{1}=2x_{2}-9
The equation is in standard form.
\frac{\left(x_{2}-7\right)x_{1}}{x_{2}-7}=\frac{2x_{2}-9}{x_{2}-7}
Divide both sides by -7+x_{2}.
x_{1}=\frac{2x_{2}-9}{x_{2}-7}
Dividing by -7+x_{2} undoes the multiplication by -7+x_{2}.
-2x_{2}+x_{1}x_{2}=-9+7x_{1}
Add 7x_{1} to both sides.
\left(-2+x_{1}\right)x_{2}=-9+7x_{1}
Combine all terms containing x_{2}.
\left(x_{1}-2\right)x_{2}=7x_{1}-9
The equation is in standard form.
\frac{\left(x_{1}-2\right)x_{2}}{x_{1}-2}=\frac{7x_{1}-9}{x_{1}-2}
Divide both sides by -2+x_{1}.
x_{2}=\frac{7x_{1}-9}{x_{1}-2}
Dividing by -2+x_{1} undoes the multiplication by -2+x_{1}.
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