Question

Use Cramer's rule to solve the system of equations.

Answer 1

Are you familiar with Cramer's rule?

Answer 2

It is a method to find the value of X and Y, and also Z in other cases.

Answer 3

ive not in the slighest clue every time i try i feel like i get it less and less

Answer 4

You were not taught this concept yet?

Answer 5

fraid not

Answer 6

http://www.purplemath.com/modules/cramers.htm Look at this, hopefully you may see some correlations, but I will help you through it.

Answer 7

Or you can check this web page:
http://www.1728.org/cramer.htm

Answer 8

@CamPayne That one is more detailed in the steps required, the one I commented does not fully show every step.

Answer 9

okay can you guys just walk me through this one a small step at a time

Answer 10

Want me to do it vurify?

Answer 11

First off, I believe you must get the x and y value on one side and the numerical value on the other.

Answer 12

so how does you do that

Answer 13

@wolf1728 If you wish, but I have knowledge of this, also I do not mind if you want to. If I do, please correct me if I make any mistakes.

Answer 14

See, you have:
6x = 2 - y
3x+1 = 2y

Answer 15

What would you do to move the y to the other side? For: 6x = 2 - y ?

Answer 16

umm i suppose you'd add y or something?

Answer 17

Correct.
Which would result into:
6x + y = 2.
Now, let's look at:
3x + 1 = 2y
Two steps for this one.

Answer 18

kay

Answer 19

Step 1
3x + 1 = 2y
Add -1 to both sides

Answer 20

3x -1 +1 = 2y -1
What does that become?

Answer 21

um 3x + y?

Answer 22

i think thats wrong

Answer 23

It is wrong - try again.

Answer 24

(-1+1) = ?

Answer 25

0

Answer 26

Which would result to:
3x = 2y - 1.
Now, we have to move the y to the other side, what would you do?

Answer 27

Also, the 2 and y will stay together.

Answer 28

Basically, you are moving 2y to the other side

Answer 29

okay

Answer 30

Just like the one incident:
What would make (2y (+/-) (value)) = 0. To cancel it out from that side and move it to the other? Would you add it, or subtract it?

Answer 31

looks like subtract

Answer 32

Correct, which would result to:
3x - 2y = -1

Now, your two equations are:
6x + y = 2.
3x - 2y = -1.

Answer 33

Now, you have to find out what is: a, b, c, d, e, and f.

Answer 34

You first count the coefficient of the x and y values then the numerical values they are equal to.

Answer 35

So, hint, a = 6, what do you think b is ?

Answer 36

a? i only see Xs and Ys

Answer 37

To use Cramer's Rule you have to think of the first equation as:
ax + by = e

Answer 38

This is in relevance to Cramer's Rule.

Answer 39

i see

Answer 40

So, what do you think b is now?

Answer 41

This will eventually help us find the determinant's numerator, which then helps us find the values of x and y.

Answer 42

-1 is b -1?

Answer 43

ax + by = e.
6x + y = 2.
3x - 2y = -1.

Answer 44

Try now.

Answer 45

so am i solving really for x?

Answer 46

You will solve for x and y, eventually, you have other steps to do beforehand.

Answer 47

We must find out the values for a, b, c, d, e, f.
There is this many variables, because there is this many values displayed.

Answer 48

How many y's is y?

Answer 49

1?

Answer 50

Yes. b = 1.

Answer 51

yay

Answer 52

ax + by = e.
6x + y = 2.
3x - 2y = -1.
a = 6, b =1, c = ?, d = ? Now look at only (3x - 2y).

Answer 53

Can you tell me what c and d = from that?

Answer 54

That should be
cx + dy = f

Answer 55

I just realized that, also, thank you.

Answer 56

cx + dy = f.
3x - 2y = -1.

Answer 57

okay soo then what? i solve for c?

Answer 58

Just find what c and d equal from what the equation states, just like a and b.
Hint c is the coefficient of x, and d is the coefficient of y.

Answer 59

C = 3. D = -2. Do you understand that?

Answer 60

not quite how is that??????

Answer 61

cx + dy = f.
3x - 2y = -1.
Coefficient means the value in front of a variable.
The value in front of x is 3.
The value in front of y is -2. (Subtraction sign makes it negative.)

Answer 62

okay but which ones are d and y?

Answer 63

C = 3. Which was the coefficient, in front of x.
D = -2. Which was the coefficient, in front of y.

Answer 64

ohhh i see now

Answer 65

So, a = 6, b = 1, c = 3, d = -2, e = ?, f = ?
The numerical values they are equal to, so then
e = 2.
f = -1.
Do you understand this part?

Answer 66

yeah i do now

Answer 67

im sorry if i seem like a lost cause

Answer 68

dn = (a • d) - (c • b)

Answer 69

What I would you about earlier, plug in those values then you will find it, this helps you solve for x and y.

Answer 70

dn = (6 • -2) - (3 • 1) = ?

Answer 71

so -12 minus 3

Answer 72

Yes, = -15.

Answer 73

kay so what do we do with that

Answer 74

x = [(e • d) - (f • b)] ÷ dn

Answer 75

a = 6, b = 1, c = 3, d = -2, e = 2, f = -1

Answer 76

x = [(2 • -2) - (-1 • 1)] ÷ -15

Answer 77

x = ?

Answer 78

Hint: double negative makes positive.

Answer 79

so 15

Answer 80

[(-4)-(-1)] / -15 = ?

Answer 81

Brackets mean you perform first.

Answer 82

-5

Answer 83

-4 + 1 / -15 = ?

Answer 84

5

Answer 85

With brackets around -4 + 1. NEGATIVE 4 PLUS POSITIVE ONE = NEGATIVE 3.

Answer 86

-3 / -15.
Is not the same as -15/-3.

Answer 87

0.2?

Answer 88

CORRECT.

Answer 89

X = 0.2
One done, now y.

Answer 90

Very good !!

Answer 91

oh boy

Answer 92

a = 6, b = 1, c = 3, d = -2, e = 2, f = -1
y = [(a • f) -(c • e)] ÷ dn

Answer 93

a = 6, b = 1, c = 3, d = -2, e = 2, f = -1
y = [(6 • -1) -(3 • 2)] ÷ -15.

Answer 94

Remember do the actions in the brackets first before dividing by -15.

Answer 95

0.8?

Answer 96

Yes, wonderful.
X = 0.2
Y = 0.8