Quadratic forms with a linear constraint

Solve the system
$3 x^{2} - 2 y^{2} + 5 z^{2} = 0,$
$7 x^{2} - 3 y^{2} - 15 z^{2} = 0,$
$5 x - 4 y + 7 z = 6.$

~10 minAnswer checked instantlyquadratic eliminationlinear substitution

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 23

Stuck? A gentle nudge

Something off?

Workspace

Your answer

Loading the math keyboard…

Type naturally — sqrt, pi, / and ^ become notation. Any equivalent form is accepted. Press Enter to check.

Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).