# How do I solve this simultaneous equation:x+y=8 x- y=1

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### 3 Answers

We'll can also solve the system of simultaneous equations using the substitution method (instead of elimination method).

For this reason, we'll extract x from the second equation:

x- y=1

We'll add y both sides and we'll get:

x = y + 1 (1)

We'll substitute x into the first equation:

x + y = 8

y + 1 + y = 8

We'll combine like terms:

2y + 1 = 8

2y = 8 - 1

2y = 7

y = 7/2 (2)

We'll substitute y in (1):

x = y + 1

x = 7/2 + 1

x = (7+2)/2

x = 9/2

**The solution of the system is the pair of coordinates (x,y): **

**(9/2 , 7/2)**

Solve the simultaneous equations:

x+y = 8......(1)

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

Solution:

We add eq (1) and eq(2) and we get:

(x+y)+(x-y) = 8+1=9

x+y+x-y = 9

2x = 9.

Divide by 2:

x = 9/2 = 4.5.

Now eq (1) - eq(2) gives: (x+y)-(x-y) = 8-1 = 7

x+y-x+y = 7

2y = 7

Divide by 2:

y = 7/2 = 3.5.

Therefore x = 4.5 and y = 3.5 are the solutions of the given equations.

Tally:

Put x = 4.5 and y = 3.5 in both equations:

First equation:

LHS x+y = 4.5 + 3.5 = 8 = RHS.

2nd equation:

LHS x-y = 4.5 - 3.5 = 1 = RHS.

x-y=1

x-y-x=1-x

-y=1-x

-y/-1=1/-1-x/-1

y=-1+x

x-1+x=8

2x-1=8

2x-1+1=8+1

2x=9

2x/2=9/2

**x=4.5**

4.5-y=1

4.5-y-4.5=1-4.5

-y=-3.5/-1

**y=3.5**