If x-3y=-9 and 5x-2y=7 what is the value of x?

2x - 6y = - 18
-15x + 6y = - 21--------ADD

- 13x = - 39
x = 3

15 - 2y = 7
8 = 2y
y = 4

x = 3 , y = 4

x - 3y = -9 (solve by using substitution)
5x - 2y = 7

x - 3y = -9
x = -9 + 3y
5x = 5(3y - 9)

5x - 2y = 7
5(3y - 9) - 2y = 7
15y - 45 - 2y = 7
15y - 2y = 7 + 45
13y = 52
y = 52/13
y = 4

x - 3y = -9
x - 3(4) = -9
x - 12 = -9
x = -9 + 12
x = 3

∴ x = 3 , y = 4

Then, Y=-9-x/-3= 9+x /3 and Y=7-5x/2,then 9+x/3=7-5x/2,18+2x=21-15x. 17x=3,x=3/17

Using simultaneous equation,

We rewrite x - 3y = -9,
into x = 3y - 9, and let this equation be called 1.

We let 5x - 2y = 7 be 2.

Substituting equation 1 into 2,

we get 15y - 45 - 2y = 7
which ends up as y = 4.

Putting this value of y back into equation 1, we get x = 3.

Please try out all the workings by your own

There are 20 different ways to solve these, I present three methods.


x - 3y = -9 ---> equation(1)
5x - 2y = 7 ---> equation(2)


Elimination Method:
------------------

Multiply equation(1) by -5


-5x + 15y = 45
5x - 2y = 7
---------------
13y = 52

y = 4

Now, substitute into equation(1) or (2) to solve for x:

x - 3y = -9

x - 12 = -9

x = 12 - 9

x = 3

Therefore, the solution is (3,4).

Substitution Method:
--------------------

x - 3y = -9 ---> equation(1)
5x - 2y = 7 ---> equation(2)

Solve for x from equation(1),

x = 3y - 9 ---> equation(*)

Substitute(*) into equation(2),

5(3y - 9) - 2y = 7

Solve for y

15y - 45 - 2y = 7

13y = 52

y = 4

Now, substitute y = 4 into equation(*),

x = 3y - 9

x = 3(4) - 9

x = 12 - 9

x = 3

(3,4) <---- Solution

Matrix Method:
-------------

x - 3y = -9 ---> equation(1)
5x - 2y = 7 ---> equation(2)

Write in the form of an augmented matrix,

[1 -3 | -9]
[5 -2 | 7 ]

Perform a LU factorization or Gaussian elimination, to get the row-reduced echelon form,

[1 0 | 3]
[0 1 | 4]

Therefore, x = 3 and y = 4 is the solution.