S.O.E. and Inequalities and adding, subtracting, multiplying and dividing monomials

System of Equations

x  |  y=4x -1 | y |  (x, y)  |

-3    4(-3) -1     -11    (3, -11)

-2    4(-2) -1    -9    (-2, -9)

-1    4(-1) -1     -5     (-1. -5)

0     4 (0) -1     -1    (0. -3)

1     4 (1) -1       3     (1, 1)

2    4 (2) -1       7     (2, 7)

3    4 (3) -1       11    (3, 11)

 

x  |  y=-x +4|   y |  (x, y)  |

-3    -(-3) +4  7     (-3, 7)

-2    -(-2) +4  6    (-2, 6)

-1    -(-1) +4   5     (-1. -5)

0     -(0) +4   4    (0. -3)

1     -(1) +4     3     (1, 1)

2    -(2) -1       2    (2, 7)

3    -(3) -1       1    (3, 11)

 

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VOCABULARY

The two lines intersect at the solution. The solution is also where the two lines overlap. Always mark the solution area with a bold S.

A system of inequalities is a two inequalities presented as a set.

To solute or not solute

Determine if coordinate (1,4) is a solution for the systems below

y=x+3            y=2x-2

4=1+3            4=2(1)-2

4=4                 4=0

CHECK           DOES NOT CHECK

The solution is not a solution for this system of equations

y=5x -1        y=-2x + 6

4=5(1)-1      4= -2(1)+6

4=4                4=4

CHECK          CHECK

The solution is a solution for this system of equations

Problem:

y=5x-1
y=-2x+6

System of Equations

System of equations (S.O.E)

The System

4x -14 = -4y         first equation

-2x -3y = -9          second equation

Step 1: Take the first equation and put it into y-intercept form (y = mx + b)

4x – 14 = -4y -x – 7/2 = y

-4           -4

Step 2: Substitute the y-value into the second equation

-2x – 3(-x – 7/2) = -9              -2x + 3x – 21/2 = -9                  x – 21/2 = -9

x – 21/2 + 21/2 = -9 + 21/2

x = 1.5

Step 3: Substitute the x-value into the first equation

4(1.5) -14 = -4y               6 – 14 = -4y                -8 = -4y

-8/-4 = -4y/-4                 

2 = y

Solution (1.5 , 2)

Step 4: Check your answer. Substitute your x and y values into both equations. In order for your answer to be correct, both equations must match.

4(1.5) – 14 = -4(2)                             -2(1.5) -3 (2) = -9

6 – 14 = -8                                            -3 -6 = -9

-8 = -8                                                   -9 = -9

CHECK!                                                 CHECK!

SYSTEM OF EQUATIONS- WORD PROBLEMS

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.