Use the method of substitution to solve the system. (If there is no solution, enter NO SOLUTION.)

Question

Use the method of substitution to solve the system. (If there is no solution, enter NO SOLUTION.)

x2

+

z2

=

17

4x

+

y

=

3

y

+

z

=

3

Smaller values x,y,z=

Bigger values x,y.z=

Answer 1

4x + y = 3

y + z = 3

We need to eliminate y, as the other equation has x and z

y = 3 - z

4x + 3 - z = 3

4x - z = 0

z = 4x

Using the other equation,

x^2 + (4*x)^2 = 17

x^2 + 16x^2 = 17

17x^2 = 17

x = 1, -1

When x = 1, z = 4x = 4

y + z = 3

y + 4 = 3

y = 3 - 4

y = -1

When x = -1, z = 4x = -4

y + z = 3

y - 4 = 3

y = 3 + 4

y = 7

(1, -1, 4)

(-1, 7, -4)