More Linear Equations

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More Linear Equations
Cramers rule derived by solving the general
system by elimination. Uses the determinant
notation.
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• a x b y e
• c x d y f
• a c x - b c y -c e
• a c x a d y a f
• ady bcy af ce
• (ad bc) y af ce
• af ce
• y ----------
• ad bc
• adx bdy de
• -bcx - bdy -bf
• adx bcx de bf
• (ad bc)x de bf

Cramer introduced the determinant notation x
y x w z y z w for a
difference of products. It make it easier to
remember what order to subtract. Cramers rule
for 2 by 2 system of linears
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Example 3 x 4 y 2 7 x 5 y
13 Another example
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Cramers Rule doesnt work when the determinant
0 Example 2x 3y 0 6x 9y
1 Another example 2x 3y 1 6x 9y 3
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Lots of questions can be answered by setting up
and solving a system of two equations in two
variables. Common
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Almost always there is more than one way to set
up the equations. Example An unknown number
is multiplied by 7 and added to 5. The resulting
number is divided into 40, and 3 is obtained.
What is the unknown number? One setup Let x
be the desired number. Then 40/(7x 5)
3 Solve for x. Another setup. Let x be the
unknown number and y be the resulting
number. Then y 7x 5 and 40/y
3. Solve for y, then for x.
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Common 4 A rectangular blue box of an
unknown height has a width of 3 in. A red box
with the same height is 12 inches wider. The
area of the red box is 5 sq in. more than three
times the area of the blue box. Then the
heights of the two boxes must be _________in.
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Like common 10 A mix of peanuts and walnuts is
to be made up and sold for 2.25 per
pound. Peanuts cost 1.00 per lb and walnuts cost
2.00 per lb. If the cost of the mix is to be
1.75 per lb., how many lbs of peanuts must there
be in 10 lbs of mix?