Explain why it isn’t always best to solve a system of equations by graphing.

Question

Please give an example in which this is the case.

Answer 1

Hi there Melonie,

 

It turns out that solving systems of equations by graphing works pretty well for 2x2 systems [aka, 2 equations in 2 unknowns] -- the kind you can draw in a plane, like this one, which you can probably solve pretty quickly:

 

x + 3y = 7

x + y = 5

 

And this one is nice enough that there's an integer solution, namely, (4, 1). You could graph this pretty easily.

 

But this gets way harder as soon as you stop having such nice numbers:

 

πx + 3y = 7

9x + sqrt(2) * y = 1

 

You could graph it, but you'd only get an approximation of the exact value, which is probably fine sometimes, but that's no good for anything where you want the exact answer (which will be in terms of pi and the square root of two).

 

Finally, if you start adding unknowns and equations, you can quickly get more complicated systems:

 

1x + 2y + 3z = 27

3x + y - 4z = 1

x + y + z = 100

 

You could graph this, but each equation represents a plane in 3D space, which is hard to visualize, and it's not even obvious that all three planes intersect in one point, or even in one line (I just made that up so I can't tell, either!)

 

And, if you add a fourth variable and equation, it becomes almost impossible to visualize -- that's the 4th dimension! It obviously gets very tedious trying to solve such big systems by algebra, but fortunately there are computer programs to do it all very quickly

 

I hope that was helpful!

Joseph

Answer 2

Because its difficult to graph 3 or more equations containing 3 or more variables on a two-axis coordinate system.