Solving 2y-4x-5=0 and y=3x+1 with matrices gives zero determinant

[BilloRani2012]

Homework Statement

Use Matrices to solve for x and y if:

2y - 4x - 5 = 0 and y = 3x + 1

Homework Equations

The Attempt at a Solution

I have done it, but i get a determinant of zero. So is this right?

My working is the following:

i rewrote both equations in the form of ax+bx = 0

so, 4x - 2y + 5 =0 and -3x + y -1 = 0

then when i find the lAl <-- determant i get zero. i think its right, because isn't it a 2x3 matrix??

 

[rl.bhat]

You have to write the equations in the form ax + by = c.
Here the determinant is
| 4 -2 |
| -3 1 |
It is not zero.

 

[BilloRani2012]

but what happens to the -5 in the first equation and -1 in the 2nd equation

 

[BilloRani2012]

okay so i did it and got the determant = 2

| 4 -2 | lxl = l-5l
| -3 1 | lyl l 1 l

 

[rl.bhat]

From the given equations, you have to write three matrices.

| 4 -2 ||x| = |-5|
|-3 1||y| | 1|
It i in the form AX = D
You can solve the equations by finding the inverse of A and multiply it with D.

 

[BilloRani2012]

okay i did it and got x = 3/2 and y = 11/2. is that right?

 

[drhassan]

to know whether you answer right or not, substitute back x=3/2 and y=11/2 in your equations and the answer should be 2(11/2) - 4(3/2) - 5 =11-6-5= 0, which means you have the right answer