how to solve algebraic equation using elimination method
how to solve algebraic equation using elimination method
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.