Rules to remember for monomials
- When you multiply coefficients, you add exponents
- When you divide coefficients, you subtract exponents
- When you raise an exponent to a power, you multiply exponents
Archive for 02/16/2011
STEPS TO SOLVING SYSTEM OF EQUATIONS WORD PROBLEMS
1. Identify the variables
2. Write the system of equations
3. Solve
4. Check your answer
5. Write your answer in a sentence to demonstrate your understanding of what you have found
example
Robert bought pizzas and sodas from Key Pizza. He purchased 2 bottles of soda for every box of pizza that he bought. The individual cost of pizza and soda is $5 and $1 dollar respectively. Robert spent a total of $56.00. How many boxes of pizzas and bottles of soda did Robert buy from Key Pizza?
step 1
x = number of pizzas, y = number of bottled sodas
step 2
2x = y
5x + y = 56
step 3
5x + 2x = 56 ——> 7x = 56 —–> 7x/7 = 56/7 —–> y = 8
2(8) = y —-> 16 = y
step 4
2(8) = 16 —-> 16 = 16—–> CHECK
5(8) + 16 = 56 —-> 40+ 16 = 56—–> 56 = 56——> CHECK
step 5
Robert bought 8 boxes of pizza and 16 bottles of soda from Key Pizza.
MONOMIALS WITH…
ONE VARIABLE
with a negative
without a negative
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MORE THAN ONE VARIABLE
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RAISE FRACTION TO A POWER
To simply: =
Without negative exponents:
COMBINING DIVISION AND RAISING TO NEGATIVE POWERS
THINGS TO REMEMBER…
- Raise whole numbers to a power
- Always solve what is in the parentheses first
- Divide your coefficients
- Multiply everything in the parentheses
x + 7y= -3 3x-2y= -9
1. Choose one of the three methods (graphing, elimination, substitution) to solve for x and y. For this example, it is best to choose the elimination method
Whether you choose to eliminate x or y, you will still receive the same end result.
-3(x+7y = -3) distribute negative two by all the numbers in the parentheses
1(3x – 2y = -9) distribute negative two by all the numbers in the parentheses
2. Rewrite the new equations so that the y values cancel out.
-3x-21y = 9 The x values are eliminated.
3x-2y = -9 Negative two y subtracted from negative twenty-one y equals negative twenty-three y. Negative nine subtracted from positive nine equals zero.
3. Solve for x by substituting your y-value into the second equation.
y=0
x + 7(0) = -3
x + 0 = -3
x = -3
Therefore, your solution is (3,0)
4. Check your answer by substituting your x and y values into the original equations.
3 + 7(0) = -3 ———> 3 +0 = -3 ———> 3 = 3 CHECK
3(-3 ) – 2( 0 ) = -9 ———-> -9 – 0 = -9 ——–> -9 = -9 CHECK
Stacy went to the store last Wednesday to purchase 13 bags of chips and 7 cases of soda. The total of her groceries was $35.25. The cost of one bag of chips and one case of soda combined was $3.75. What is the price of one bag of chips and one case of soda?
STEP 1 Identify your variables.
x= bags of chips
y= cases of sodas
STEP 2 Write your two equations.
x + y = $3.75
13x + 7y = 35.25
STEP 3 Solve.
x + y = 3.75 ———> x-x +y = -x + 3.75 ———-> y = -x + 3.75
substitute y = -x + 3.75 into your second equation.
13x + 7(-x + 3.75) = 35.25 ——–> 13x -7x + 26.25 = 35.25 ——> -4x + 26.25 = 35.25 ——->
-4x + 26.25 – 26.25 = 35.25-26.25 ——> -4x = 9.00 —–> -4x/4 = 9.00/4 —–> x= 1.5
substitute 1.5 for x into your first equation.
1.5 + y = 3.75 —–> 1.5 – 1.5 + y = 3.75 ——> y = 3.75-1.5 —–> y = 2.25
STEP 4 Check your answer.
1st equation 1.5 + 2.25 = 3.75 —–> 3.75 = 3.75 CHECK
2nd equation 13(1.5) + 7(2.25) = 35.25 ——> 19.5 + 5.75 = 35.25 ——> 35.25 = 35.25 CHECK
STEP 5 Answer your question by writing a sentence.
The price of one bag of chips is $1.50. The price of 1 case of soda is $2.25.
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