Question

SOLVE FOR Y:
x = 7y
x + y + z = 80
2x - y + z = 105

A. -7
B. 15
C. -175/13
D. 35
E. none of these

Answer 1

ok

Answer 2

This one i think is D? i know you have to solve by substitution.

Answer 3

Take the first equation x = 7y, and replace x in the second equation with that

Answer 4

7y + y + z = 80
2(7y) - y + z = 105

I replaced X in the second 2 equations with x= 7y, good with that so far?

Answer 5

yes.

Answer 6

now you have 2 equations with 2 unknowns Y and Z,, we can solve this by a couple methods

Answer 7

adding the Y's to simplify a little bit

8Y + Z = 80
13Y + Z = 105

Answer 8

we can multiply one of the equations by a constant number and then add them together,

Answer 9

here, if you multiply one of them by -1, then when you add them you get +Z-Z = 0 the Z will go to zero

Answer 10

(-1)(8Y + Z = 80 ) multiply first by -1
13Y + Z = 105
-------------------

-8Y - Z = -80
13Y + Z = 105 ADD the two together
--------------
5Y + 0Z = 25 no Z's Left now

5Y = 25 divide by 5 both sides

Y = 5

Answer 11

Do you recall doing this kind of thing in class?

Answer 12

okay that's what i was getting as well, i got 35 for x 5 for y and 40 for z when i did it.

Answer 13

yes we did this in class.

Answer 14

ok, just want to make sure i am using a similar method to what you are learning...

Answer 15

Now that you figured Y=5, you can use that in the first equation to get X

X = 7Y = 7*5 = 35

X=35

Answer 16

Now you know X and Y, use any of the last 2 equations to get Z

Answer 17

which would come to z = 40, right?

Answer 18

Using equation 2,

x + y + z = 80 and X=5 , Y = 35

5 + 35 + z = 80

z = 40

yep

Answer 19

alright :) i'm glad i'm doing this correctly then. so the right answer would be E for this then.

you're the best!! would you mind helping me with the other one as well?

Answer 20

If you wanted to check after you finished, use

x=5
y=35
z=40

plug those into all 3 equations and see if they all are true

Answer 21

oh, Y=5, X=35, Z=40. typo above

Answer 22

okay! thank you. im glad that i know this method correctly.

Answer 23

Right , answer is NONE, Y=5

Answer 24

cool, welcome, anytime