SOLUTION: Write a system of the form ax+by=c dx+ey=f where a,b,c,d,e, and f are consecutive integers. Solve the system and make a conjecture. Please help! this

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Question 221030: Write a system of the form
ax+by=c
dx+ey=f
where a,b,c,d,e, and f are consecutive integers. Solve the system and make a conjecture.

Please help! this is taken fron the textbook Beginning Algebra By Addison WEsley
Answer by ankor@dixie-net.com(12704) About Me  (Show Source):
You can put this solution on YOUR website!
Write a system of the form
ax+by=c
dx+ey=f
where a,b,c,d,e, and f are consecutive integers. Solve the system and make a conjecture.
:
1x + 2y = 3
4x + 5y = 6
:
Multiply the 1st equation by 4, subtract the 2nd equation from it:
4x + 8y = 12
4x + 5y = 6
--------------eliminate x
3y = 6
y = 2
then use the 1st equation to find x
x + 2(2) = 3
x = 3 - 4
x = -1
;
:
Check solutions in the 2nd equation
4(-1) + 5(2) = 6
-4 + 10 = 6
:
:
Can we conjecture that any system like this will have solutions
x = -1 and y = 2