Given that these simultaneous equations x - y = k
x² + y² – 9=0
have exactly one pair of solutions, show that k = +3V2.

Thank you for the help :)

See explanation

Step-by-step explanation:

The two linear equations can be solved simultaneously;

4x+3y=8 (1)

−2x−3y=−4---(2)

If we multiply equation (1) by 1 and equation (2) by (2)

We have;

4x+3y=8 (3)

-4y - 6x = 4 ---(4)

Adding equation (3) and (4)

-3x = 12

x= -4

Substitute x = -4 into equation (1)

4(-4) + 3y = 8

-16 + 3y = 8

3y = 8 + 16

y= 24/3

y= 8

Hence;

x= -4 and y =8