# 2x+3y+7z=13 3x+2y-5z=-22 5x+7y-3z=-28

2x+3y+7z=13 3x+2y-5z=-22 5x+7y-3z=-28

## Solution by Cramer's rule

body preview (19 words)

To solve xxxx equation xxx be xxxx Cramer's xxxxx

x attach xxx xxxxxxxx in xxx xxxx of x xxxxx

file1.doc preview (189 words)

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

To solve xxx above equation xxx xx used Cramer's Rule.

**AX x B**

x is xxx xxxxxxxxxxx xxxxxxxx

X is x xxxxxx vector.

x xx x vector.

xxx xxxxxxxx xx xx x xx x A

For xxxx case xxxxxxxx**
**

**xxx **

B = xxxxx xxxxxxxxx xxxxxxxx xxxx xxx equation.

xxxx xxxxxxxx by xxxxxxxxx xxx first column xx the xxxxxx A xx xxx constant vector x

Ay = xxxxxxxx by xxxxxxxxx xxx second column xx the matrix A xx the constant vector B

xxxx xxxxxxxx xx xxxxxxxxx xxx third column of the xxxxxx A by xxx xxxxxxxx xxxxxx B

The next xxxx xx xx calculate xxx xxxxxxxxxxx xx xxxx xxxxxxx

xxxx = x xx

|Ax| = x xxxx

|Ay| = x -174

|Az| = x 261

xxxxxxxxxxx xxx value xx x, y xxx x can be xxxxxxxxxxx

xxxx |Ax| / |A|

= -87 / xxx

xxx xxx

xxxx |Ay| x xxxx

= -174 x 87

xxx -2

z = xxxx x xxxx

= xxx x xxx

Thus xxxxxxxx xxxxxxxx xxx y, z) = xxxx xxxxxx

Note:

If there are less obvious, xxx xxx xxxxxxxxxxx xxxx pm xx xxxx

xxxxx you.

the coefficient of x

the xxxxxxxxxxx of y

xxx xxxxxxxxxxx of z

# _1392475990.unknown

# xxxxxxxxxxxxxxxxxxx

# xxxxxxxxxxxxxxxxxxx

# xxxxxxxxxxxxxxxxxxx

# _1392476204.unknown

# _1392476054.unknown

# xxxxxxxxxxxxxxxxxxx

# _1392475826.unknown

# _1392475339.unknown

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## The solution is (x,y,z) = (-1,-2,3).

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2x+3y+7z = 13

xxxxxxxx = -22

xxxxxxxx x xxx

1. Pick a letter xx eliminate and xxx equations that xxxxxxx xxxx xxxxxxx

x will arbitrarily pick the letter y xx xxxxxxxxx and I xxxx arbitrarily

pick the xxxxxxxxxx

3x+2y-5z = xxx

xxxxxxxx = -28

to eliminate x from.

xxxxx the xxxxxxxxxxxx of x xxx x xxx 7, xxxxxxxx the first

xxxxxxxx xxxxxxx xx xx xxx the second xxx xxxxxxx xx x xx

they will have coefficients xxxx will cancel when equals are

xxxxx to xxxxxxx

xxxxxxxxxxxx x xxx

xxxxxxxx 6z = -56

-------------------

-11x +29z x 98

2. Next, eliminate that same letter from one xx xxxxx xxxxxxxx

xxx the equation you xxx not use in xxxx 1.

I did not xxx

2x+3y+7z = xx

xx xxxx 1. I will use it with

xxxxxxxx x xxx

to eliminate the xxxx xxxxxx xx

3x+2y-5z = xxx

2x+3y+7z x 13

Multiply the first xxx xxxxxxx xx xx xxx xxx xxxxxx

xxx xxxxxxx by 2:

xxxxxxxxxx x xx

4x+6y+14z = xx

xxxxxxxxxxxxxxx

xxx xxxx x xx

xx xxx you have x xxxxxx xx xxxx two equations xx two letters:

-11x+29z x 98

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