How to Simplify a Matrix Equation?

[helpm3pl3ase]

x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -tIam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.

 

[mathman]

x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -t


Iam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.

Your notation is confusing. You have a blank in the first equation between 2y and y. Similarly in the second equation between 3z and 4y. What do you mean??

 

[helpm3pl3ase]

The two are separate matrices

Like one is
x+2y y+2t
4x+3z 4y+3t

And the other is
5x -y
5z -t

And they set them equal and simplify to

z = 2x, t = -y

I don't get how they got that?

 

[EnumaElish]

You have a 4x4 matrix on the left.

What is on the right?

 

[helpm3pl3ase]

I have no 4x4

one matrix is 2x2:

(First column)
x+2y
4x+3z
(Second Column)
y+2t
4y+3t

Second matrix is 2x2:

(First column)
5x
5z
(Second Column)
-y
-t

 

[HallsofIvy]

x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -t


Iam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.

Now that we have it clear that these are matrices, they must give, since two matrices are equal if and only if their corresponding entries are equal,
x+2y= 5x, y+ 2t= -y, 4x+ 3z= 5z, and 4y+ 3t= -t.
The third equation is just 4x= 2z (subtract 3z from both sides). Also, the fourth equation is the same as 4y= -4t (subtract 3t from both sides) so t= -y as claimed.

 

[helpm3pl3ase]

Ahh I understand now... Thank you so much for the help.