how to solve algebraic equation using elimination method

how to solve algebraic equation using elimination method

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x + y = 8 eq. 1

2x = y - 5 eq. 2

move variables around fo eq. 2 so it will have same form as eq. 1:

2x - y = -5 eq. 3

add eq. 1 to eq. 3:

x + y = 8

2x - y = -5

3x = 3

x = 1

lets use eq. 1 to figure out y value by substituting value of x:

1 + y = 8

y = 8 - 1

y = 7

therefore** x = 1, y = 7**

The first equation has x and y on the left with a constant on the right. Let's change the second equation to match that format:

2x = y-5

-y -y

2x - y = -5

Now, we can take our original first equation and add it to the new format of the second:

x + y = 8

2x - y = -5

Notice that the y and the -y cancel each other out, leaving us with only x as a variable.

(x+2x) + (y-y) = 8+(-5)

3x = 3

Divide both sides by 3:

x = 1

Now, substitute 1 in for x in either of the original equations. Let's use the first one, since it is a little simpler than the other:

x+y = 8

1+y = 8

-1 -1

y = 7

So, the final answer is x=1, y=7.