solve the simultaneous equations below?

Step one is to get the equations into the form ax + by = c
for i) this is 3x + y = 2 and -x+3y =16

Next, create a 2x2 matrix 'A' by placing the values of x in the equations in the first column and the values of y in the second column so we get

3 1 = A
-1 3

this matrix is then set up in an equation such that
| x | * A= | 2 |
| y | . |16|

Now you need the inverse matrix. To get this we need the determinant of A (detA) as well as the transpose of A (Atrans).

The determinant ends up being (3)*(3) - (1)(-1) = 10

The transpose of a 2x2 matrix is found by switching the top left and bottom right values and multiplying the bottom left and top right values by -1... example:

The transpose of
a b is d -b
c d -c a

That having been said, Atrans =
|3 -1|
|1 3|

The formula for the inverse of matrix A is:
A(inv) = (1/det) * Atrans

therefore we get A(inv) =
|.3 -.1|
|.1 .3|

We then multiply both sides of our original matrix equation using basic matrix rules and we get:

|1 0| * | x | = | -1 |
|0 1| . | y | | 5 |

which says that x = -1 and y = 5. Plug this into both of your original equations and you get the correct answer.

Do the exact same thing for part two and you should get
x = -1 and y = 1

If you need anything clarified, feel free to message me.

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1)x=-1,y=5

-3y+1=0 3y= 1 y= 1/3 x(2)-3x(1/3)+1/3(2)=11 2x -x =11-2/3 x= 31/3 or did were u supposed to write x^2-3xy+y^2=11???

1)
y = 2 - 3x
3y - x = 16

y = 2 - 3x
3y = 3(2 - 3x)

3y - x = 16
3(2 - 3x) - x = 16
6 - 9x - x = 16
-10x = 16 - 6
-10x = 10
x = 10/-10
x = -1

y = 2 - 3x
y = 2 - 3(-1)
y = 2 - (-3)
y = 2 + 3
y = 5

∴ x = -1 , y = 5

= = = = = = = =

2)
5x - 2y = -7
3x/4y - 1 = 0

5x - 2y = -7
2y = 5x + 7
4y = 2(5x + 7)

3x/4y - 1 = 0
3x/(10x + 14) = 1
3x = 10x + 14
3x - 10x = 14
-7x = 14
x = 14/-7
x = -2

5x - 2y = -7
5(-2) - 2y = -7
-10 - 2y = -7
2y = -10 + 7
2y = -3
y = -3/2 (-1.5)

∴ x = -2 , y = -3/2 (-1.5)

for part (i), the answer is

x = -1, y = 5

for part (ii), if the equation is 3x/4y - 1 = 0, then the answer is

x = -2, y = -1.5

part a
x= -1
y= 5

part b
x = -1
y = 1

As has already been solved, (i) x=-1, y=5
(ii) x=-1, y=1

(i)
6 - 9x - x = 16
- 10x = 10
x = - 1

y = 2 + 3
y = 5

x = - 1 , y = 5

(ii)
10x - 4y = - 14
3x + 4y = 1------ADD

13x = - 13
x = - 1

-10 - 4y = - 14
- 4y = - 4
y = 1

x = - 1 , y = 1

1)x=-1
y=5

(i)
the answers:
x=1
y=5

(ii)
the answers:
x= -1
y=1