Question

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

Answer 1

you can put the system in its matrix form, and if the inverse matrix exists, the system has only one solution

Answer 2

i know it has one solution but how do i get the solutions

Answer 3

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

Answer 4

I apologize, my value of x was not correct. Rather, it should be 6.

Answer 5

Final answer:
x = 6
y = -3

Answer 6

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

Answer 7

so in what case do you add both equations instead of solving for x?

Answer 8

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.

Answer 9

ohkay! thanks!

Answer 10

your welcome

Answer 11

so with 2x − y = 5
3x+ y= −6

Answer 12

x = 1/5

Answer 13

y=3?

Answer 14

your x should be -1/5 so if you plug that back in, y = -27/5 I think.

Answer 15

i got 26/5 and it was right

Answer 16

Check it with the other equation. I'm guessing it won't work.

Answer 17

you are right the equation gave me some weird number