Question

Solve the following system by your choice of method
3xsquared + 3ysquared=19
5xsquared - 4ysquared=16

Answer 1

\[\left\{3 x^2+3 y^2=19,5 x^2-4 y^2=16\right\} \]Replace x^2 with u and y^2 with v.\[\{3 u+3 v=19,5 u-4 v=16\}\]Solve the above for u and v.\[\left\{u=\frac{124}{27},v=\frac{47}{27}\right\} \]\[\left\{x^2=\frac{124}{27},y^2=\frac{47}{27}\right\} \]\[\left\{x=\pm \sqrt{\frac{124}{27}},y=\pm \sqrt{\frac{47}{27}}\right\} \]There are four combinations of (x,y) pairs.