Proving the Uniqueness of Solutions for Linear Equations with Real Coefficients

[brad sue]

Hi,
Please can someone help me with this problem.

show that a,b,c are real numbers and a#0, then there is a unique solution of the equation ax+b=c.

the uniqueness of the solution is my problem.
Thank you
B

 

[HallsofIvy]

If the uniqueness is the problem, then suppose there were two solutions, x₁ and x₂. Since they are solutions to that equation, you must have, of course, ax_{1+ b= c and ax2+ b= c. Subtracting one equation from the other, a(x1- x2)= 0. What does that tell you?}

 

[brad sue]

If the uniqueness is the problem, then suppose there were two solutions, x₁ and x₂. Since they are solutions to that equation, you must have, of course, ax_{1+ b= c and ax2+ b= c. Subtracting one equation from the other, a(x1- x2)= 0. What does that tell you?}

_{That's right. we can ay that x1=x2. so unique soltuion
thanks}