Solve using any method:
2x - 7y = 540
14x + 3y = 120
Since there are no 1 or -1
coefficients, the easiest way
is by elimination.
(This is sometimes called
"addition method" or the
"addition-subtraction method".)
Eliminate x by multiplying the
first equation thru by -7 and the
bottom equation thru by 1. Then
add vertically:
-7[ 2x - 7y = 540]
1[14x + 3y = 120]
-14x + 49y = -3780
14x + 3y = 120
--------------------
52y = -3660
y = -915/13
That is the value for y
However it is very difficult to
substitute such a god-awful
fraction as that. So start over
and eliminate y by multiplying the
first equation thru by 3 and the
bottom equation thru by 7. Then
add vertically:
3[ 2x - 7y = 540]
7[14x + 3y = 120]
6x - 21y = 1620
98x + 21y = 840
-------------------
104x = 2460
x = 2460/104
x = 615/26
That's the value of x
Even though they are
terrible fractions, they
caused no difficulty since
instead of substituting,
we started over and
eliminated the other variable.
Answer (x,y,) = (615/26, -915/13)
Edwin
