SOLUTION: Find two systems of linear equations that have the ordered pair (-2,1) as a solution.

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Question 1193490: Find two systems of linear equations that have the ordered pair (-2,1) as a solution.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The simplest such system of two equations is

    x = -2

    y = 1.

Solved.

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By the way and for your better understanding,

        first equation determines vertical line  x= -2;
        second equation determines horizontal line  y= 1.

The intersection point of these lines is the given point  (-2,1).




Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


Ikleyn's was indeed the easiest possible answer.  But you are to 
find TWO SYSTEMS. Ikelyn has only given you one system.  I'll show 
you how to find a second system.

But instead of doing it for you, I'll do one exactly like it but
change the ordered pair.  I'll do this one instead:
Find two systems of linear equations that have the ordered pair
(-3,2) as a solution.
Make up 4 easy numbers at random for coefficients.
I'll arbitrarily pick 4,3,2, and -5 to use for 
coefficients of x and y for the left sides of two 
equations. Put blanks to be filled in on the right 
side of each equation:

system%284x%2B3y=%22___%22%2C2x-5y=%22___%22%29

Now, to the side, we determine what two numbers to put in the blanks
on the right, by substituting the given ordered pair's coordinates 
for x and y in the left sides.

left side of first equation: 4x+3y = 4(-3)+3(2) = -12+6 = -6 

So we put a -6 in the first blank:

system%284x%2B3y=-6%2C2x-5y=%22___%22%29

Substitute in the other left side

left side of second equation = 2x-5y = 2(-3)-5(2) = -6-10 = -16 

So we put a -16 in the second blank:

system%284x%2B3y=-6%2C2x-5y=-16%29

That's the system. Now do your problem the 
same way.  Maybe you like Ikleyn's simple 
solution, but you might want to make up 
another one like this.

Edwin