Question

I don't know how to do it, so you need to help me out here. Solve each system of equations, and show your work/steps:

12. 2x - y = 2
3z = 21
4x + z = 19

14. 5x + 2y = 4
3x + 4y + 2z = 6
7x + 3y + 4z = 29

Answer 1

12.
Start off by solving for z

3z=21
z=7

Answer 2

You can use this z value to plug into the equation 4x+z=19 in order to solve for x

4x+7=19
4x=12
x=3

Answer 3

Finally, plug in your x value into the equation 2x-y=2 in order to solve for y

2(3)-y=2
6-y=2
y=4

Answer 4

This method is known as the substitution method and is one way of solving systems of equations

Answer 5

did you subtract 2 or 6

Answer 6

I subtracted 6 from 2
-y=-4
negatives cancel out
y=4

But subtracting 2 from 6 would work as well
4-y=0
y=4

Answer 7

wouldn't you get y = -4, if I subtracted 2

Answer 8

You would subtract 2 from 6, and be left with 4-y=0
Add the y to the other side → y=+4

Answer 9

@Copythat What would I do here

Answer 10

The easiest method for solving 14. is elimination

Answer 11

14. 5x + 2y = 4
3x + 4y + 2z = 6
7x + 3y + 4z = 29

[5x+2y=4]*3 → 15x+6y=12
[3x+4y+2z=6]*4 → 15x+16y+8z=24

15x+6y=12
-15x+16y+8z=24
____________________
-10y+8z=-12

Answer 12

I took the first two equations and multiplied the first by the x value in the second and the second by the x value in the first. Your goal here is to eliminate the x variable.

Answer 13

(3x + 4y + 2z = 6)*-5

Answer 14

[3x+4y+2z=6]*5 → 15x+20y+10z+30

Once you have both of your new equations, you subtract in order to eliminate your x variable

Answer 15

@Copythat understand

Answer 16

Its not a mistake. Subtracting 15 from 15 gives you 0.

Answer 17

If you multiply by -5, then you must use addition to eliminate x

Answer 18

no you don't

Answer 19

Why? You now have a new equation which you can use to plug into the third equation and solve for another variable

Answer 20

(5x + 2y = 4)*3 ----> 15x + 6y = 12
(3x + 4y + 2z)*-5 =6 --> -15x - 20y - 10z = -30

15x + 6y = 12
-15x - 20y -10z = -30
0x - 14y - 10z = -18

Answer 21

@ajprincess What do I do now???

Answer 22

Nw take the two eqns 5x + 2y = 4 and 7x + 3y + 4z = 29.
Eliminate x terms from both eqns. Can u do that @Firejay5?

Answer 23

Yea I'll give it a shot and come back with an answer

Answer 24

ha k. 5n:)

Answer 25

35x + 14y = 28
-35x -15y - 20z = -130

-y - 20z = - 102

Answer 26

is that correct @ajprincess

Answer 27

29*-5=-145

Answer 28

35x + 14y = 28
-35x -15y - 20z = -145

-y - 20z = - 117

Answer 29

- 14y - 10z = -18
-y - 20z = - 117
Nw try eliminating y from both the eqns. Can u do it @FireJay5?

Answer 30

yes

Answer 31

after doing it solve for z. k?

Answer 32

you should've gotten -130, not -145

Answer 33

What is 29*-5=?