Answer to Question #7799 in Abstract Algebra for Rita

Question

Part 2

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. Use the example on page 426 of Mathematics in Our World as a guide.
Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra?

Answer 1

Let's take 4 and 7. Let's construct equations. We take x,y as variables. So, e.g. let's construct the first equation as x+y. Since our solution is 4,7 the right part must be 4+7=11. So we have the first equation.
The second equation let's take as 2x-y. The right part must be 2*4-7=1. Therefore the system is the following:
x+y=11
2x-y=1
To solve it let's add two equations:
3x=12 whence x=4
y=11-x=7