# SOLUTION: Hello, I have linear equation problem that I am stuck on. I have tried the problem myself but I'm having trouble with it. Here is the problem I'm working on: Determine the nece

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Hello, I have linear equation problem that I am stuck on. I have tried the problem myself but I'm having trouble with it. Here is the problem I'm working on: Determine the nece      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Matrices, determinant, Cramer rule Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Matrices-and-determiminant Question 398712: Hello, I have linear equation problem that I am stuck on. I have tried the problem myself but I'm having trouble with it. Here is the problem I'm working on: Determine the necessary conditions on a, b and c for the following systems to have: a unique solution; an in finite number of solutions; or be inconsistent. x1 + ax2 = 5 3x1 + 6x2 = b Here is the work I've done so far, and this is all in matrices so imagine the boxes around the numbers: 1 a |5 3 6 |b multiplying row 2 by 1/3 1 a | 5 1 2 | b/3 subtracting row 1 from row 2 1 a |5 0 2-a |b/3 - 5 I'm not sure if what I've done is correct, but this is where I'm stuck because I do not know how to set up the three conditions? Thank you for any help YuryAnswer by stanbon(57347)   (Show Source): You can put this solution on YOUR website!Determine the necessary conditions on a, b and c for the following systems to have: a unique solution; an in finite number of solutions; or be inconsistent. x1 + ax2 = 5 3x1 + 6x2 = b --- Put in slope-intercept form: x1 = -ax2 + 5 slope = -a int = 5 --------- x1 = -2x2 - (b/3) slope = -2 int = (-b/3) ============================ Unique solution when slopes are not equal: -a is not equal to -2 a is not equal to 2 -------------------- Inconsistent when slopes are equal. -a = -2 a = 2 --------------- Infinite # of solutions when slopes and int are equal. a=2 and (-b/3) = 5 b = -15 =================== Cheers, Stan H.