Is it possible to get two unknown variables in this equation

[nau]

Is it possible to get x,y (unknown variables)
using a,b,c,d, and r (all real numbers).

Equation: Sqrt( ( (a+bx)-(c+dy) )^2 ) = r

 

[Dr.Peterson]

Is it possible to get x,y (unknown variables)
using a,b,c,d, and r (all real numbers).

Equation: Sqrt( ( (a+bx)-(c+dy) )^2 ) = r

If you mean, can you solve this one equation to obtain unique solutions for both x and y, the answer is no. For any value of x, you can solve for a value or two of y, but there will be many pairs that work.

There are times when one equation can be solved for two (real) variables; one case would be sqrt(x^2 + y^2) = 0. But that is rare.

Are you aware that the equation you wrote is equivalent to |(a+bx)-(c+dy)| = r, and therefore to |bx - dy + a-c| = r? Its graph will be two lines, not one point.