simultaneos equation ??? help?

6x+y=25
2x+y=13
----------
- - -

6x - 2x = 25 - 13

4x = 12

x = 3 <<<< Substitute in any of the equation:

6(3) + y = 25

18 + y = 25

y = 25 - 18

y = 7

Solution set {3, 7}

6x + y = 25
- 6x - 3y = - 39-----ADD

- 2y = - 14
y = 7

6x + 7 = 25
6x = 18
x = 3

x = 3 , y = 7

6x + y = 25 (solve by using elimination)
2x + y = 13

...6x + y = 25
‒ 2x + y = 13 (subtraction)
------------------------
4x = 12

4x = 12
x = 12/4
x = 3

2x + y = 13
2(3) + y = 13
6 + y = 13
y = 13 - 6
y = 7

∴ x = 3 , y = 7

6x + y = 25 Eq. (1)
2x + y = 13 Eq. (2)
----subtract------
4x = 12
x = 12/4
x = 3

6x + 3y = 39 Eq. (2) x 3
6x + y = 25 Eq. (1)
----subtract------------
2y = 14
y = 14/2
y = 7

(x, y) = (3, 7)

2x + y = 13
x = (13 - y)/2
Substitute for x in the first equation
6(13-y)/2 + y = 25
3(13-y) + y = 25
39 -3y +y = 25
2y = 39-25
2y = 14
y = 7

x = (13-y) /2
x = 6/2
x = 3

6x+y=25
y=25-6x
put this value in 2nd eq

2x+y=13
2x+ (25-6x)=13
2x+25-6x=13
-4x=13-25
-4x=-12
x=(-12)/(-4)
x=3

now put this value of x in 1st equation
6x+y=25
6(3) +y=25
18+y=25
y=25-18
y=7

so x =3 & y=7

On Adding
6x+y=25 & -2x-y=-13

4x = 12
x = 3

Use one of the equations to find y.
6(3)+y=25
y = 7

Multiply the 2nd equation by (-)
then add them, then the result
3x=12
x=4
and substitute x in any of the 2 equations
2(4)+y=13
then y=5

#1: 6x+y=25
#2: 2x+y=13

#3: 8x+2y=38 ==> Merge 2 equations together

4x
=(6x+y) - (2x+y) ==>Take equation 1 minus #2
=25-13
=12

x=3

y
=13 - (2*3)
=13-6
=7

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