anonymous
  • anonymous
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x− 5y=39 2x+3y=3
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
you can put the system in its matrix form, and if the inverse matrix exists, the system has only one solution
anonymous
  • anonymous
i know it has one solution but how do i get the solutions
anonymous
  • anonymous
you can divide by 3 the 2nd equation, substract y, and multiply by 3/2 on both sides, and then substitute x on the first equation

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KingGeorge
  • KingGeorge
I apologize, my value of x was not correct. Rather, it should be 6.
KingGeorge
  • KingGeorge
Final answer: x = 6 y = -3
KingGeorge
  • KingGeorge
To repeat my method to make it more clear, multiply the second line by 2, so you have 4x+6y = 6. Then you can subtract line 2 from line 1, leaving you with 0x-11y = 33 so y=-3 then plug y=-3 back in, and get 2x+3(-3) = 3 so 2x=12 so x =6. Final solution: x = 6 y = -3
anonymous
  • anonymous
so in what case do you add both equations instead of solving for x?
KingGeorge
  • KingGeorge
Both methods work, but since you only had to multiply a single line to get a 4x in both equations, I consider this method faster. For example, if the bottom line were 45x+3y=3, I would have solved for y instead of adding the equations.
anonymous
  • anonymous
ohkay! thanks!
KingGeorge
  • KingGeorge
your welcome
anonymous
  • anonymous
so with 2x − y = 5 3x+ y= −6
anonymous
  • anonymous
x = 1/5
anonymous
  • anonymous
y=3?
KingGeorge
  • KingGeorge
your x should be -1/5 so if you plug that back in, y = -27/5 I think.
anonymous
  • anonymous
i got 26/5 and it was right
KingGeorge
  • KingGeorge
Check it with the other equation. I'm guessing it won't work.
anonymous
  • anonymous
you are right the equation gave me some weird number

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