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Mathematics - Writing Equations











































Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.

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Sep 14, 2011
Mathematics - Writing Equations
by: Staff

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Part II

5. Check your answer


Check the answer. Solve the two equations using the addition/subtraction method. The solutions should be: x = -7, y = 2


x + 3y = -1

5x - y = -37

Multiply the 2nd equation by 3

3*(5x - y = -37)

3*5x - 3*y = 3*(-37)

15x - 3y = -111

The two equations are now:

x + 3y = -1

15x - 3y = -111

Add the two equations to eliminate the y variable:

x + 3y = -1

+ (15x - 3y = -111)
------------------------
x + 15x + 3y + (- 3y) = -1 + (- 111)

x + 15x + 3y - 3y = -1 – 111

Combine like terms

(x + 15x) + (3y - 3y) = (-1 – 111)

(16x) + (0) = (-112)

16x + 0 = -112

16x = -112

Divide each side of the equation by 16

16x/16 = -112/16

x*(16/16) = -112/16

x*(1) = -112/16

x*1 = -112/16

x = -112/16

x = -7


Substitute -7 for x in either of the two original equations, and then solve for y.

x + 3y = -1

-7 + 3y = -1

Add 7 to each side of the equation:

-7 + 3y + 7 = -1 + 7

Combine like terms:

-7 + 7 + 3y = -1 + 7

(-7 + 7) + 3y = (-1 + 7)

(0) + 3y = (6)

0 + 3y = 6

3y = 6

Divide each side of the equation by 3

3y/3 = 6/3

y*(3/3) = 6/3

y*(1) = 6/3

y*1 = 6/3

y = 6/3

y = 2


when the two equations are solved algebraically, the solution is:

x = -7

y = 2

These values match the original integers selected at the beginning of the problem. Therefore, the equations are valid.



Thanks for writing.

Staff
www.solving-math-problems.com



Sep 14, 2011
Mathematics - Writing Equations
by: Staff


Part I

The question:

Select any two integers between -12 and +12 which will become solutions to a system of two equations.

Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.

Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.


The answer:


The five steps are:

1. Understand what the problem is asking you to do
2. Identify the information provided (known and unknown information)
3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)
4. Solve the problem
5. Check your answer


Applying these 5 steps to your problem:

1. Understand what the problem is asking you to do

(The first two sentences in the problem statement tell you what to do.)

Select two integers between -12 and +12

Write two equations that have your two integers as solutions.



2. Identify the information provided (known and unknown information)

Known Information

- The two integers you select.

Unknown Information

- two equations that have your two integers as solutions


3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)

You can randomly pick any two integers. As an example, pick: -7, 2

Although the equations haven’t been written yet, the solution will be:

x = -7

y = 2


4. Solve the problem


The easiest way to write the equations asked for is: 1) to begin with the solution, and 2) then work backwards.

The solution is:

x = -7

y = 2

The next step is only limited by your imagination.

The statement of the problem specifies that the equations you write must be solved by the addition/subtraction method. Therefore, you should probably write linear equations.

You can now write ANY two expressions involving the two integers (-7 and 2). However, the expressions cannot include any variables. They must be limited to arithmetic.

As an example, you could write:

1st expression:

5*(-7) - 2 = -37


2nd expression

-7 + 3*2 = -1


x = -7, and y = 2

Replace every -7 in the two expressions with x. Replace every 2 in the two expressions with y.


1st expression:

5*(-7) - 2 = -37

5*(x) - y = -37

5x - y = -37



2nd expression

-7 + 3*2 = -1

x + 3*y = -1

x + 3y = -1


The two equations are:

x + 3y = -1

5x - y = -37


The final answer to your question is:

Two integers:

-7, 2

The two equations are:

x + 3y = -1

5x - y = -37

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