Question

what is the solution of the system of equations?
-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9
and could i please get a step by step solution so i can really teach myself how it was done? thanks!!
the choices are (5,-2,7), (-5,2,7) (5,2,-7) and no solution

Answer 1

please help im really confused!

Answer 2

You want to reduce the number of variables by adding the equations together. Start by multiply eq. 1 by 2/3 and add it to eq.2

Answer 3

why by 2/3?

Answer 4

The easiest way to solve this is to try plugging in the points.

Answer 5

is it like (x,y,z) ?

Answer 6

Also, as a possible hint, for each equation the co-efficient of the x variable is the same as the coefficient for the z variable.

Answer 7

This is not the best problem to do for teaching yourself how to solve systems of equations in three variables. Doing this one will only confuse you.

Answer 8

You need to try systems that actually have solutions.

Answer 9

But I will provide you with a step by step solution since that is what you ask for.

Answer 10

okay im going to really still try to teach my self still because im still struggling and i need to know how to do these so itll really help thank you!

Answer 11

Pair the 1st and 3rd equations together:
-3x-4y-3z=-7
5x-2y+5z=9

Pair the 2nd and 3rd equations together.
2x-6y+2z=3
5x-2y+5z=9

Answer 12

ohh, okay thank you so much! im gonna take note of this.

Answer 13

For the 1st and 3rd equations, multiply 5x - 2y + 5z = 9 by -2
-3x - 4y - 3z = -7
-10x + 4y -10z = -18

Combine both equations together to get:

-13x - 13z = -25

For the 2nd and 3rd equations, multiply 5x -2y + 5z = 9 by -3
2x-6y+2z=3
-15x+ 6y-15z=-27


Combine both together to get

-13x -13z = -24


So after all that you end up with

-13x - 13z = -25
-13x - 13z = -24

This is not possible.