Question

Use Cramer's rule to find the solution of the system of equations. Write your answer as an ordered pair.
3x+y=5
2x-3y=18

Answer 1

-4

Answer 2

get the determinant first
3 1
2 -3
the determinant is -9-2=-11.
then just replace the variable you want to solve for with the answer like in the other problem.
so it would be
5 1
18 -3 to find x
which wold be -33.
and then you divide that by the det, which is -11 so x=-33/-11=3
x=3
3 5
2 18
which =44
44/-11=4
y=-4

Answer 3

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Answer 4

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Answer 5

I think I'll add a little more to that so it is easier to see Cramer's rule at work.

3x+y=5
2x-3y=18
a = 3
b =1
c = 2
d = -3
e = 5
f = 18

We first have to find a denominator determinant
dn = (a • d) - (c • b)

dn = (3•-3) -(2•1)
dn = -11

Next we have to figure the x determinant and divide it by dn
x = [(e • d) - (f • b)] ÷ dn
x = (5*-3) -(18 •1) / -11
x = -15 -18 / -11
x = -33 / -11
x = 3

Now for the y determinant
y = [(a • f) -(c • e)] ÷ dn
y = (3 • 18) -(2 • 5) / -11
y = 54 -10 / -11
y = 44 / -11
y = -4

Source:
http://www.1728.org/cramer.htm