## giselle3214 3 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

1. estebananaya

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

2. giselle3214

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

3. estebananaya

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

4. KingGeorge

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

5. KingGeorge

Final answer: x = 6 y = -3

6. 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

7. giselle3214

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

8. 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.

9. giselle3214

ohkay! thanks!

10. KingGeorge

11. giselle3214

so with 2x − y = 5 3x+ y= −6

12. giselle3214

x = 1/5

13. giselle3214

y=3?

14. KingGeorge

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

15. giselle3214

i got 26/5 and it was right

16. KingGeorge

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

17. giselle3214

you are right the equation gave me some weird number