Algebra II: Solving System of Equations Help?

Question

Solve Each System of Equations: (please show the process to the best of your ability)

17.
5x+7y=-1
-2y+3z=9
7x-z=27

18.
r-s+3t=-8
2s-t=15
3r+2t=-7

During class we learned to pick 2 equations and solve by using substitution & elimination. I know how to solve with 2 equations I'm just not sure which ones to pick.

Answer 1

17.
5x+7y=-1 (1)
-2y+3z=9 (2)
7x-z=27 (3)
(3)*3
21x-3z=81
-2y+3z=9
adding
21x-2y=90 *7
147x-14y=630
10x+14y=-2
157x=628
x=4
sub in (1)
y=-3
subin (2)
z=1


18.
r-s+3t=-8 (1)
2s-t=15 (2)
3r+2t=-7 (3)

(2)*2 4s-2t=30
3r+2t=-7
adding
4s+3r=23
(2)*3 6s-3t=45
r-s-3t=-8
adding
5s+r=37
4s+3r=23
15s+3r=111
subtracting
11s=88
s=8
sub in (2)
16-t=15
t=1
sub in (3)
3r+2=-7
r=-3

Answer 2

Yes, that's all you can do here at this level of your math career, is to pick two then solve by substitution and elimination. (If you were in linear algebra, you would solve using matrix arithmetic.)

There's no trick to determining which two equations to start off with. Any of them would do. If you see two equations where the coefficient of one term is an integer multiple of the other, that might make things a little easier to start with. Otherwise, I would just start out with any two, then plug-n-chug from there.

For 17, I think I'd start out with the 2nd and 3rd equations, because I'd only have to do one multiplication (multiply 3rd equation by 3). For 18, there's no clear-cut choice. I'd probably start with 2nd and 3rd equations here too.

You said you knew how to solve these, so I'm assuming you don't need me to show you the actual work. If you do want the solutions too, please click my avatar and send me an email, and I will come back and solve.

Hope this helped!

~ ♥ ~

Answer 3

doesn't really matter which one you pick first because they are relative to each other. In this case, i just randomly choose 2 and 3, and i like to get rid of z
-2y+3z=9
21x-3z=81
add them up
21x-2y==90
choose the first equation because they also have x and y
147x-14y=630
10x+14y=-2
add them up
157x=628
x=4
sub 4 for x
5(4)+7y= -1
20+7y= -1
7y= -21
7= -3

7(4) -z=27
28-z=27
-z= -1
z=1

ans: (4,-3,1)
now you try the second one.

Answer 4

it is comparable to what you be attentive to. you nonetheless do substitution, you only ought to do it two times... -4p + 3q + 2r = -8 p = 2q 2q - 4r = 14 This one is quite ordinary simply by fact the 2nd equation is a provide away.. Use the 2nd equation as your first substitution: -4(2q) + 3q + 2r = -8 2q - 4r = 14 Now you have 2 equations and 2 unknowns. Use the substitution which you already be attentive to to finsh this.