# Solve the following simultaneous equations. x – 2y = 6 , x + 2y = 8

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We have to solve the following set of simultaneous equations:

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

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

(2) - (1)

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

=> 4y = 2

=> y = 2/4

=> y = 1/2

substitute in (1)

x - 2y = 6

=> x = 6 + 2y

=> x = 6 + 2*(1/2)

=> x = 6 + 1

=> x = 7

**We get x = 7 and y = 1/2**

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

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

We will solve using the elimination method.

We will add (1) + (2).

==> 2x = 14

Now we will divide bu 2.

==> x = 7

Now we will substitute into (1) to determine y.

==> x - 2y = 6

===> 7 - 2y = 6

==> -2y = -1

==> y= 1/2

**Then the answer is the pair ( 7, 1/2)**

(1) x - 2y = 6

(2) x + 2y = 8

(1) + (2)

2x = 14 (This method is called elimination since we eliminated one of the variables by manipulating the equations.)

Now its single variable and you can solve for x. Plug this into one of the other equations and solve for y.

We can solve the system using substitution method, also:

We'll re-write the first equation:

x = 6+2y (1)

We'll substitute (1) in the 2nd equation:

6+2y+2y = 8

We'll combine like terms and we'll isolate y to the left side:

4y=8-6

4y=2

y=1/2

We'll substitute y in (1):

x = 6+2/2

x = 6+1

x = 7

**The solution of the system is the pair of coordinates: (7 ; 1/2).**