simultanious equation?

Question

64 + 16L + 4M = 0 and 48+8L + M = 0

I have to find the value of M and L,
can somebody talk me through it please :) thanks

Answer 1

64 + 16L + 4M = 0 -------{1}and 48+8L + M = 0 -------{2}
48+8L+M=0
M= - (48+8L)
putting the value in {1}
64+16L-4(48+8L)=0-------{EQUATION 1}
64+16L-192-32L=0
-16L-128=0
L=-8
M=48+8(-8)
M=-16

Answer 2

The method involves subtracting equations, but first you
manipulate one or the other so that when you subtract
it gets rid of either the M or L term.

Looking at the first equation we have 16L. The 2nd equation
has 8L. If we mutiply the 2nd equation by 2, we can get a
16L term:

2(48+8L +M) = 2*0

or
96 + 16L + 2M = 0

now we can subtract this new equation from the 1st one:

64 + 16L + 4M = 0
- (96 + 16L + 2M = 0)
------------------------------
-32 + 2M = 0

and we can see that M must be 16

you can then go back to either of the original equations and
replace M by 16.

48 + 8L + M = 0 becomes 48 + 8L + 16 = 0
or 64 + 8L = 0

from this we can see that L must be -8

Alternatively, you could have eliminated the M term. The easiest way to do this would be to divide the 1st equation
by 4 making it: 16 + 4L + M = 0

You could then subtract this new equation from the 2nd one
giving 32 + 4L = 0 and once again you would see that
L = -8.

Answer 3

64 + 16L + 4M = 0
48+8L + M = 0

multiply equation B by 2 and get:

A) 64 + 16L + 4M = 0
B) 96+16L + 2M = 0

Then subtract equation B from equation A, and get:

-32 + 2M = 0

Solve for M, and get:

M = 16

now use equation A, and M=16 to solve for L:

64 + 16L + 4(16) = 0

L = 0
.............
M = 16 :
L = 0 :
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