HOW TO SOLVE TWO EQUATIONS using the Substitution Method

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HOW TO SOLVE TWO EQUATIONS using the Substitution
Method 1) Solve one equation for x or y. (if not
already done) 2) Substitute the solved equation
into the other equation. 3) Solve for unknown 4)
Substitute found value into either of equations
(if not already done) 5) Solve for remaining
unknown (if not already done) 6) Check
it. ex x y 4 x y 1
(y1) y 4 2y 4 y 2 x
y 1 x 21 3 (3,2)
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Solve the following equations using the
Substitution Method ex y 0 x y 2
ex y x 1 2x y 3
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Equation of a line can be written in two ways
1) General (standard) form Ax By C
ex 5x 8y 3
A 5 B 8 C 3 ex
-4x 2y .5 A B
C 2) Slope intercept form y
mx b mslope by-intercept
ex y 3x 8
m 3
b 8

ex y _ 1 x 4 3 m
b
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Equation of a line can be written in two ways
Always put equations in slope-intercept form by
solving for y. ex Convert to slope intercept
form and then function notation 6x 2y 8
6x 2y 8 -6x -6x
2y -6x8 y -3x4 ex Convert to slope
intercept form and then function notation 3y
2x 12 ex Find
m and b given the following equation 7x 5y
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• Mike wants to save money as much as possible this
  month. Each month, he earns at the most 6000 and
  spends at least 4200.
• Let W denote the Mikes income this month. Let E
  denote the money spent this month. Let Z denote
  the amount of money Mike saves each month. Now,
  try to formulate this simple problem into math
  formulas
• Give the model you created, explain what is the
  objective function, constraints, decision
  variables, and parameters.

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• Amherst Dairy. Inc. produces three products
  pasteurized milk, yogurt and butter.
• In February, Amherst Dairy has 100 tons of raw
  milk available.
• It takes one unit of raw milk to produce one unit
  of pasteurized milk, two units of raw milk to
  produce one unit of yogurt, and eight units of
  raw milk to produce one unit of butter.
• The maximum demand for yogurt is 20 tons per
  month. The maximum demand for butter is 10 tons
  per month. The demand of pasteurized milk is
  unlimited. In order to keep the market share,
  Amherst Dairy has to at least produce 40 tons of
  pasteurized milk each month.
• The profit of the one ton pasteurized milk is
  1,000, one ton yogurt is 2,200 and one ton of
  butter is 10,000. Amherst Dairy wants to
  maximize the total profit in February.
• Give the model, and explain what is the
  objective function, constraints, decision
  variables, and parameters.

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• Iron Works, Inc. manufactures two products made
  from steel and just received this month's
  allocation of 2000 pounds of steel. It takes 2
  pounds of steel to make a unit of product 1 and 3
  pounds of steel to make a unit of product 2.
• Let x1 and x2 denote this month's production
• level of product 1 and product 2, respectively.
• Denote the unit profits for products 1 and 2
• to be 100 and 200, respectively.
• Iron Works has a contract calling for at
• least 60 units of product 1 this month. The
  firm's facilities are such that at most 720 units
  of product 2 may be produced monthly.
• Give the model, and explain what is the
  objective function, constraints, decision
  variables, and parameters.