SOLUTION: I need help with this problem. : 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 in

Question 552106: I need help with this problem. :
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. Make sure you show the necessary 5 steps.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let's take 2 integers at random.
we'll use -3 and 9
we'll let x = -3 and y = 9
let's take one equation at random.
we'll take 5x + 6y = z
when x = -3 and y = 9, this equation becomes:
5(-3) + 6*9 = z which results in:
z = 39
our first equation becomes:
5x + 6y = 39
now lets take any other equation at random.
let's try -15x - 30y = z
when x = -3 and y = 9, this equation becomes:
-15x - 30y = -225
we now have 2 equation that can be solved simultaneously.
they are:
5x + 6y = 39
-15x - 30y = -225
if we did this right, then solution should be x = -3 and y = 9.
let's see how we did.
if we multiply the first equation by 3, we get:
15x + 18y = 117 (first equation multiplied by 3)
-15x - 30y = -225 (second equation)
if we add both these equations together, we get:
-12y = -108
if we divide both sides of this equation by -12, we get:
y = 9
so far so good.
we go back to the original equations of:
5x + 6y = 39 (first equation)
-15x - 30y = -225 (second equation)
substituting 9 for y in the first equation gets:
5x + 54 = 39
solving for x in the first equation get:
x = -3
substituting 9 for y and -3 for x in the second equation gets:
-15(-3) - 30(9) = -225 which becomes:
45 - 270 = -225 which becomes:
-225 = -225
this confirms the values of x = -3 and y = 9 is a solution to both equations.

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