Question

Consider the system of equations: x + y + z = 210; x + z = 230; x + y = 120 What is the value of x?

Answer 1

First set up a system of linear equations.
x + z = 230
x + y = 120
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2x + y + z = 350

Now, set up a new system.

2x + y + z = 350
x + y + z = 210
What can you do to the second equation to eliminate x and y?

Answer 2

3x+2y+2z=560

Answer 3

Umm...no. What do you do to the second equation so that WHEN you add them, the y and z's cancel?

Answer 4

im not sure boss i told my instructor i was having problems with these and she just gave me websites to look at

Answer 5

2x + y + z = 350
x + y + z = 210
What happens when you multiply the entire second equation by -1?

Answer 6

it just negates itself

Answer 7

Yeah.
2x + y + z = 350
-x - y - z = -210
Now add the equations together and see what happens.

Answer 8

x=140

Answer 9

Yup. Look at the question. It asks for the value of x. So, there you have it. Do you understand why we multiplied the second equation by -1 though?

Answer 10

to negate or get rid of the y and z

Answer 11

You multiply by -1 so that the y and z cancel out when you add them. THis is a process called elimination.

Answer 12

you help out tremendously and explained so i can understand thank you so much

Answer 13

so it ends up 140+-20+90=210 and checks out

Answer 14

given x + y + z = 210 and x+ z = 230

then (x + z) + y = 210 or 230 + y = 210

y = -20

and x + y = 120

then x - 20 = 120

x = 140

Answer 15

Yeah. What @campbell_st did is something called substitution.

Answer 16

thanks fellas

Answer 17

np :)