# Find the simultaneous solution of these system of equations: 1. 2x=4y= 6 3x-y= 2 2. 2x=3y= 8 x=8y= 17 3. x=8= 0 2x=4y= 4

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Solving the system of equations:

- 2x+4y= 6....(1)

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

(1)+ 4*(2)

=> 2x+4y + 12x - 4y = 6+ 8

=> 14x = 14

=> x=1

Substituting x=1 is (2)

=> 3 -y =2 => y=1

**Therefore (1,1) is the result.**

- 2x+3y= 8....(1)

- x+8y= 17...(2)

(1)-2*(2)

=>2x+3y -2x-16y=8-34

=> -13y =-26

=> y=2

Substituing y=2 in x+8y=17

=> x+ 16 =17

=> x=1

**Therefore the result is (1,2)**

- x+8= 0.....(1)

- 2x+4y= 4.....(2)

From (1) x= -8

Substituting x= -8 in (2)

-16 + 4y = 4

4y = 20

y= 5

**Therefore the result (-8, 5)**

*To solve the equations:*

*1. 2x-4y= 6 (Editted)*

**3x-y= 2**

**From the 2nd equation, 3x-2y = 2, we get 3x-2 = y ansd we substitute in the first equation: 2x-4(3x-2) = 6.**

**2x-12x+2 = 6**

**-10x = 6-2 = -4.**

**x = -4/-10 = -0.4.**

**substituting in the 2nd equation 3x-y = 2, **

**3(-.4)-y = 2. **

**y = -1.2-2 = -3.2.**

**2. 2x-3y= 8**

**x-8y= 17**

**From the 2nd eq, x-8y = 17, we get x = 17+8y. Substitute this value of x in the first: 2(17+8y)-3y = 8**

**34+16y -3y = 8**

**13y = 8-34 =-26**

**y = -26/13 = -2**

**Put y = -2 in the 2nd equation, x-8y = 17 and we get x-8(-2) = 17**

**x +16 =17**

**x = 17-16 = 1.**

**x = 1 and y = -2 are the solutions.**

** **

**3.**

** x-8= 0**

**2x-4y= 4**

**The first equation gives x =8. So x = 8 is the solution.**

**Substitute x = 8 in the 2nd equation, 2*8 -4y = 4.**

** So -4y = 4-2*8**

**-4y = 4-16 = -12**

**y = -12/-3 = 4.**

**So x = 8 and y = 4 are the solution.**

We'll solve the first system using elimination method:

2x+4y= 6 (1)

3x-y= 2 (2)

We'll multiply (2) by 4 and we'll get:

4(3x-y)= 4*2

We'll remove the brackets:

12x - 4y = 8 (3)

We'll add (1) to (3):

2x + 4y + 12x - 4y= 6+8

14x = 14

We'll divide by 14:

**x = 1**

We'll substitute the value of x in (2) and we'll get:

3*1-y= 2

3 - y = 2

We'll subtract 3 both sides:

-y = 2-3

-y = -1

We'll multiply by -1 both sides:

**y = 1**

**The solution of the first system is {(1 , 1)}.**

We'll solve the second system of equations using the elimination method, also:

2x+3y= 8 (1)

x+8y= 17 (2)

We'll multiply (2) by -2:

-2x - 16y = -34 (3)

We'll add (3) to (1):

2x + 3y - 2x - 16y = 8 - 34

We'll combine like terms:

-13y = -26

We'll divide by -13 both sides:

**y = 2**

We'll substitute y = 2 in (2):

x+8y= 17

x + 16 = 17

We'll subtract 16 both sides:

x = 17 - 16

**x = 1**

**The solution of the second system is {(1 , 2)}.**

We'll solve the third system of equations using the substitution method:

x-8= 0 (1)

2x-4y= 4 (2)

We'll add 8, both sides, in (1):

**x = -8**

We'll substitute x = -8 in (2):

-2*8-4y= 4

-16 - 4y = 4

We'll add 16 both sides:

-4y = 4 + 16

-4y = 20

We'll divide by -4 both sides:

**y = -5**

**The solution of the third system is {(-8 , -5)}.**