Show that the system of equations has infinitely many soluti

Show that the system of equations has infinitely many solutions. Specify exactly the solutions and the limitations (Bonus: Graph the solutions) x^2 + y^2 = 3 2x^2 - y^2 + z^2 = 4 4x^2 + y^2 + z^2 = 10

Solution

Let x² = a , y² = b and z² = c

The matrix can be solved as below :

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -3

Eliminate the 2nd column

Let z² be any real number , y² = (2/3) + (1/3)z² and x² = (7/3) - (1/3)z²

	X1	X2	X3	b
1	1	1	0	3
2	2	-1	1	4
3	4	1	1	10