# How do find x= y= z= w=?

-2x - 1y + 2z + 2w = -15

-2x - 2y + 1z + 0w = -13

Relevance

You cannot find all of the variables. You need one equation for each variable, you have 2 equations and 4 variables.

You could, at best, find each variable in terms of 2 of the other variables.

• -2x - 1y + 2z + 2w = -15

-2x - 2y + 1z + 0w = -13

There are too many variables and not enough equations to give a unique answer

Let w = -1

Now:

-2x - 1y + 2z - 2 = -15

-2x - 1y + 2z = -13 = -2x - 2y + 1z

-2x - 1y + 2z = -2x - 2y + 1z

2z - y = z - 2y

z = -y

-2x - 2y + 1z + 0w = -13

-2x + 2z + 1z + 0w = -13

-2x + 3z + 0w = -13

-2x - 1y + 2z + 2w = -15

-2x + 1z + 2z + 2w = -15

-2x + 3z + 2w = -15

and as we decided w was -1 earlier

-2x + 3z = -13

So we could decide z was -5 and x was -1

(-2 * -1) + (3 * -5) = -13

and y = -z so y = 5

x = -1

y = 5

z = -5

w = -1

Once again, this is only one possible solution

Another possible one, from observation is:

x = 4

y = 1

z = -3

w = 0

-2x - 1y + 2z + 2w = -15

-8 - 1 - 6 + 0 = -15

-2x - 2y + 1z + 0w = -13

-8 - 2 - 3 + 0 = -13

So there are at least two different, but correct combinations. So proof by contradiction that there is not a unique solution to this problem

• -2x - 1y + 2z + 2w = -15

substitute (because x = y = z = w, I can put an x where these variables were)

-2x - 1x + 2x + 2x = -15

simplify

-3x + 4x = -15

x = -15

• Since there are four variables, there will be four answers. Use the transitive postulate for this.

Have fun plugging and chugging!

Source(s): C_3252.ew
• ROTFLMSFAO!!!!!!!!!!!!!

You really are totally lost. Quite wasting bandwidth and go back to 1'st year Algebra. And this time, *learn* something instead of just fumbling around and squeeking through the class.

Doug

• Anonymous

[ matrix ]

_ _ _ _

| -2 -1 2 2 | ^(-1) X | -15 | = no possible answer

|_-2 -2 1 0 _| |_-13 _|

• Anonymous

You cant solve that there are too many variables and not enought information

• Anonymous

-(-2x-y+2z+2w=-15)

-2x-2y+z+0w=-13

==============

2x+y-2z-2w=15

-2x-2y+z+0w=-13

==============

2(y-2z-2w=15)

-2y+z+0w=-13

==============

2y-4z-4w=30

-2y+z+0w=-13

==============

-4z-4w=30

4(z+0w=-13)

==============

-4z-4w=30

4z+0w=-52

=========

-4w=-22

w=22/4=5.5

4z+0(5.5)=-52

4z=-52

z=-13

-2x-y+2(-13)+2(5.5)=-15

-2x-2y+(-13)+0(5.5)=-13

==================

-2x-y-26+11=-15

-2x-2y-13+0=-13

============

-(-2x-y-15=-15)

-2x-2y-13=-13

============

2x+y+15=15

-2x-2y-13=-13

============

2x+y=0

-2x-2y=0

=======

-y=0

y=0

-2x-0+2(-13)+2(5.5)=-15

-2x-0-26+11=-15

-2x-15=-15

-2x=0

x=0

(0,0,-13,5.5)

Check:

-2(0)-1(0)+2(-13)+2(5.5)=-15

-26+11=-15

-15=-15

-2(0)-2(0)+(-13)+0(5.5)=-13

-13=-13