Pam K.

asked • 10/06/12# equations that I created. Want to see if they are correct.

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.Solve your system of equations by the addition/subtraction method.

The solutions are 12 and 6

addition equation:

x-3=3

x-6+0=3+3

x+0=6

x+6

check:

x-0=6

6-0=6

6=6

subtraction method:

x + 6=12

x +6-6=12-6

x+0=6

x=6

check:

x + 6= 12

6+6=12

12=12

## 2 Answers By Expert Tutors

Scott T. answered • 10/17/12

Math and Science Tutoring from an MIT Masters in Engineering

Hi Pam,

An easy way to create a system of equations is to start just how you started, by choosing a value for x (looks like you chose 6) and y (looks like you chose 12).

Then just write an expression involving x and y, for example, I pulled this expression out of thin air:

2x - 3y

What would 2x - 3y equal if we knew that x was actually (6) and y was actually (12)?

2(6) - 3(12) = 12 - 36 = -24

So you're first equation could be: 2x - 3y = -24

Choose another expression to make a second equation. I'm going to use:

-5x + 2y

If x is 6 and y is 12, again, then -5(6) + 2(12) = -30 + 24 = -6

Your second equation could be: -5x + 2y = -6

It's not a magical equation - you could choose any expression you want to make your own!

Now you've got:

(1) 2x - 3y = -24

(2) -5x + 2y = 6

The next step is to pretend you don't know what x and y are and solve this system of equations!

I hope this technique for generating a system of equations is helpful to you. Remember: two equations means two unknowns!

ST

John R. answered • 10/09/12

John R: Math, Science, and History Teacher

A system of equations is two (or more) equations in which the solution in which the same set of values for the variables satisfies all of the equations.

As a simple example, the two equations could be x + y =2 and x - y = 0. The solution for the system of equations is x = 1 and y =1.

Now an example of how to work the problem (feel free to use my steps, but change the numbers so that you do your own work).

I am going to pick to two integers between -12 and 12. In case, I will use 3 and -1.

I am now going to make up two problems that involve multiplying 3 by something and adding it to -1 multiplied by something and solve them

4 X **3** +2 X **(-1)** 2 X **3** - 1 X **(-1)**

12 -2 6 + 1

10 7

Using these answers, I rewrite the problems, substituting x for 3, y for -1, and set them equat to the answers.

4x + 2y = 10 2x - y = 7

The system of equations is **1.** 4x + 2y = 10 and **2.** 2x - y = 7 (the bold numbers are for identifying the equations later. They are not part of the equation)

There are three methods of solving this equation: Graphing, Elimanation, and Substitution. Your question requires the elimination method (called addition/subtraction).

To solve a system of equations using elimination method, you will need to add or subtract a multiple of one equation from a multiple of the other so that one of the variables will be multiplied by zero (and be eliminated).

In my example, the sign on the y terms is opposite and the coefficient on **1.** is twice the size of the coefficient on **2.** If I multiply **1.** by one (leave it the same) and multiply **2.** by two, I can add them together and get a coefficient of 0 on the y term. (See below)

1 X **1. **4x + 2y = 10 = 4x + 2y = 10

2 X **2. **2(2x - y) = (2)7 = 4x - 2y = 14

8x + 0y = 24

The result of adding the two equations is 8x + 0y = 24. Now we solve the equation to find x.

8x + 0y = 24

8x + 0 =24

8x = 24

x = 3

Once one of the terms (the value of x or y) is found, you just need to substitute it into one of the equations to find the other term. For example, we can substitue 3 for x in **1.** to get 4 X 3 + 2y = 10.

4 X 3 + 2y = 10

12 + 2y = 10

2y = -2

y = -1

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Quynh N.

You need to find a system of 2 equations and 2 variables (x and y).

10/08/12