Question

Please help!
a+b=5
b+c=-2
c+a=7
Solve

Answer 1

you can isolate 'a' in the third equation

c+a=7
c+a-c=7-c ... subtract 'c' from both sides
a = 7-c

then plug this into the first equation

a+b=5
7-c+b=5 ... replace 'a' with 7-c
7+b-c = 5
7+b-c-7 = 5-7 ... subtract 7 from both sides
b-c = -2

Answer 2

after doing all that, we end up with this system of equations

b+c=-2
b-c = -2

do you see what to do next?

Answer 3

I understand so far but I don't know what to do next.

Answer 4

try adding the 2 equations and what do you get ?

Answer 5

notice that the c's cancel

Answer 6

b=-4 ?

Answer 7

yep

Answer 8

you forgot to add the b terms

b+b = 2b

Answer 9

oops..my bad....sorry, I missed that

Answer 10

so if 2b = -4, then b = ???

Answer 11

b=-2

Answer 12

yes....now sub -2 in for b in the other equations to find the other letters

Answer 13

a=7 and c=0 ?

Answer 14

so we have this claim

a = 7
b = -2
c = 0

let's test that claim with each equation


Testing equation 1:
a+b = 5
7+(-2) = 5 ... plug in a = 7 and b = -2
5 = 5 ... true


Testing equation 2
b+c = -2
-2+0 = -2 ... plug in b = -2 and c = 0
-2 = -2 ... true


Testing equation 3
a+c = 7
7+0 = 7 ... plug in a = 7 and c = 0
7 = 7 ... true


All three equations are true when a = 7, b = -2 and c = 0. So the solution (a,b,c) = (7,-2,0) is confirmed

Answer 15

whenever you get a possible solution, it's always a good idea to check that possible solution back into the original equation(s) to see if it's a true solution or not

Answer 16

okay thank you so much!

Answer 17

you're welcome