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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
 2 years ago
 2 years ago
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
 2 years ago
 2 years ago

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estebananayaBest ResponseYou've already chosen the best response.0
you can put the system in its matrix form, and if the inverse matrix exists, the system has only one solution
 2 years ago

giselle3214Best ResponseYou've already chosen the best response.0
i know it has one solution but how do i get the solutions
 2 years ago

estebananayaBest ResponseYou've already chosen the best response.0
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
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
I apologize, my value of x was not correct. Rather, it should be 6.
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Final answer: x = 6 y = 3
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
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 0x11y = 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
 2 years ago

giselle3214Best ResponseYou've already chosen the best response.0
so in what case do you add both equations instead of solving for x?
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
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.
 2 years ago

giselle3214Best ResponseYou've already chosen the best response.0
so with 2x − y = 5 3x+ y= −6
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
your x should be 1/5 so if you plug that back in, y = 27/5 I think.
 2 years ago

giselle3214Best ResponseYou've already chosen the best response.0
i got 26/5 and it was right
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.2
Check it with the other equation. I'm guessing it won't work.
 2 years ago

giselle3214Best ResponseYou've already chosen the best response.0
you are right the equation gave me some weird number
 2 years ago
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