Posted by Amy on Friday, October 17, 2008 at 11:08pm.
Substitution method:
6x+5y=17
x=53-8y
Solve for a variable and substitute it in to one of the equations. The easiest way with these two equations is to take x from the second equation and substitute it in to the first equation.
6(53-8y)+5y = 17
618 - 48y + 5y = 17
-48y + 5y = 17 - 618
-43y = -601
y = -601/-43
Then you plug y in to one of the equations and solve for x.
x = 53 - 8*(601/43)
Elimination method: The idea is you multiply one equation by a constant so either x or y has the same coefficient as the x or y in the other equation.
Example:
#1) x + 3y = 4
#2) 5x + 2y = -19
We need to pick a variable to eliminate. The easiest way is to eliminate the x in the second equation. To do this we multiply the first equation by 5 and subtract it from the second.
5*(x+3y) = 5*4
5x+15y = 20
It's tricky to write out the next part online, you normally write the equations directly over each other with a subtraction sign.
5x + 2y - 5x - 15y = -19 - 20
-13y = -39
At this point you can easily solve for y.
y = -39/-13 = 3
Then substitute y=3 in to one of the first equations.
x + 3y = 4
x + 3*3 = 4
x + 9 = 4
x = 4 -9
x = -5
--The problem you gave is slightly different.
2x+3y=5
4x+6y=10
In this problem you'd multiply the first equation by 2 and subtract it from the second. The new second equation is then 0 = 0.
This set of equations is not solvable. Using the elimination method one of the equations is completely eliminated because they are equivalent equations.
how do you do this equation by using elimination.? 8x-5y=11
4x-3y=5