math problem?

Question

Solve each system of equations using matrices. If the system has no solution, say it is inconsistent.

{2x + 3y = 7
{3x - y = 5

Can you explain how you solve this so I understand? it is in the system of linear Equations: Matrix Method! I need it in row echelon form then give solution for y and x?

The solution of the system is x = 2 and y = 1

I just want to know how you solve this so you get the solution?

Answer 1

it will be like this..
2 3 7 ----> r2 - r1=new r1
3 -1 5


1 -4 -2 -----> r2-3r1=new r2
3 -1 5


x y
1 -4 -2
0 11 11

so..
11y = 11
y=1

den subst.
x -4 = -2
x= -2+4
x= 2

Answer 2

The matrix should be:

{ 2 3 {x = {7
3 -1} y} 5}

Find inverse of {2 3
3 -1}:
determinant = 1/((2)(-1)-(3)(3))
= -1/11
Since determinant >0 , there is no solution

Answer 3

From you equation
3x - y = 5
y = -5 - 3x

Using
2x + 3y = 7
2x + 3(-5 - 3x) = 7
2x -15 - 9x = 7
-7x = 22
x = -22/7

Using y = -5 - 3x
y = -5 -3(-22/7)
y = -5 -66/7
y = -35/7 - 66/7
y = -101/7