corner point, linear progrmming: economic approach

[asoom]

hello, everyone im really bad in math so
i need help with the corner points

2x + 5y= 36
10x + y = 36

step one is to multiple by (-5) then we will get -10x-25y=-180

then we add the second equation with this -10x-25y=-180

-24y=-144
y=144/24=6

i would like to know why did we multiple by (-5) ?

 

[JeffM]

hello, everyone im really bad in math so
i need help with the corner points

2x + 5y= 36
10x + y = 36

step one is to multiple by (-5) then we will get -10x-25y=-180

then we add the second equation with this -10x-25y=-180

-24y=-144
y=144/24=6

i would like to know why did we multiple by (-5) ?

Because when we multiply 2x by - 5 we get - 10x and when we add 10x and -10x we eliminate x from the system of equations.

You think backwards. How can I reduce this system to one equation with one unknown. I see that 10x is 5 times 2x. And to eliminate x I need an equation with -10x so - 5 is the magic bullet.

This is just one way to solve systems of simultaneous equations. It happens to be very quick for some systems, but it is a mess for others. Denis showed you the method that works well every time.

 

[JeffM]

Btw, why in heck are you calling this:
corner point, linear progrmming: economic approach

I suspect the linear equations represent constraints in a simple linear programming problem, and he needs to find corner points to feed into his objective function. Why someone would take linear programming without knowing how to solve systems of simultaneous linear equations is beyond me, but people do odd things every day.