Question

Solve the following system of equations using matrices.
x = -2y + 6
2x + 2y = 16

Answer 1

****This will give you half credit at least.****
[1 2] [x]=[9]
[1 1] [y] [1]

A^-1=1/(ad-bc)

A^-1=1/-1 [1 -2]
[-1 1]

A^-1=[-1 2]
[1 -1]

[-1 2] [1 2] [x]= [-1 2] [9]
[1 -1] [1 1] [y] [1 -1] [1]

(-1x1)+(2x1)=1
(-1x2)+(2x1)=0
(1x1)+(-1x1)=0
(1x2)+(-1x1)=1

(-1x9)+(2x1)= -7
(1x9)+(1x1)=10

[1 0] [x]= [-7]
[0 1] [y] [10]
x= -7
y= 10

(-7)-2(10)=-27 Not 9 X Wrong!!!
(-7)+(10)=-3 Not 1 X Wrong!!!

If I solve not using matrices.
x-2y=9
x+y=1
-x -x
x-2y=9
y=-x+1
x-2(-x+1)=9
Distribute
x+2x-2=9
Combine like terms.
3x-2=9
Subtract 2 on both sides.
3x=7
Divide by 3 on both sides.
x=2 1/3
Substitute 7 into x+y=1
so...
(7)+y=1
Subtract 7 on both sides.
y=-6
(7)-2(-6)=9 7-12= -5 Not 9 X Wrong!!
(7)+(-6)=1 7-6=1 Yes 1 Right!!!
What is it that I just can't get the question completely right? I tried two methods and can't seem to find my own mistake...

Answer 2

I have (-2, 10)