Question

PLEASE HELP! 30 POINTS for RIGHT answer!


For the system below:

(a) Solve the system by linear combination method. Show all work carefully.

(b) Check your answer.

m - 2n = 2
m + n = 2(n - 3)

Answer 1

gg easy

we want to cancel 1 term

first, get them into form am+bn=c where a, b, and c are constants

m-2n=2 is good

m+n=2(n-3) is m+n=2n-6 which is m-n=-6

compare constants

m's have 1 and 1

n's have -2 and -1

let's cancel m's

a. multiply 1st equation by -1

-m+2n=-2

add to 2nd equation

-m+2n=-2

m-n=-6 +

0m+n=-8

n=-8

sub back

m-n=-6

m-(-8)=-6

m+8=-6

m=-14

b. to check

m=-14 and n=-8

m-2n=2

-14-2(-8)=2

-14+16=2

2=2 yep

m-n=-6

-14-(-8)=-6

-14+8=-6

-6=-6 yep

so m=-14 and n=-8 is the solution