SOLUTION: Consider the system of linear equations x + 3 y = a 2x + by = 8 where a and b are real numbers. I am asked to determine what values of a and b give a unique soluti

Algebra.Com
Question 881132: Consider the system of linear equations
x + 3 y = a
2x + by = 8 where a and b are real numbers.
I am asked to determine what values of a and b give a unique solution.
If I am correct I know that b cannot equal 6. How do I prove this answer though?
Thank you

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
For infinitely many solutions, the second equation is a multiple of the first equation.
Multiply equation 1 by 2.

So
or
and
or
.
.
.
The other case is an inconsistent system that has no solution. That happens when
but has any other value than because then the two lines are parallel.
.
.
.
So to have a unique solution, can take on any value other than
and can take on any value.

RELATED QUESTIONS

Q) Consider the system of linear equations x + 3y = 5 (answered by rothauserc)
My question is in reference to one involving "Solving systems of linear equations by the... (answered by Earlsdon)
Consider the system of equations x + 2y - 3z = a 2x + 6y - 11z = b x - 2y + 7z = c... (answered by MathLover1,math_tutor2020)
Consider the system y = a and x = b where a and b are real numbers. Is this system... (answered by jim_thompson5910)
Consider the system y = a and x = b where a and b are real numbers. Is this system... (answered by jim_thompson5910,ewatrrr)
consider the system y=a and x=b where a and b are real numbers. Is this system dependent... (answered by Fombitz)
Consider the system y=a and x=b where a and b are real numbers. Is this system dependent (answered by richard1234)
Consider the system y=a and x=b where a and b are real numbers. Is this system... (answered by robertb)
I am trying to solve the linear system of equations by graphing. the problem reads... (answered by mananth)