Using the Elimination method...Algebra?

Question

I have to use the elimination method to find the soultions (x and y)...The problem is: 7x-3y=13; 5x-2y=27

Answer 1

OK: so first line them on one over another:
7x - 3y = 13
5x - 2y = 27

Now what you want to do is either eliminate the x's or the y's, by finding a common multiple--in this case it's easier to do the y's
Muliply the top equation by -2, and the bottom equation by 3:

-14x + 6y = -26
15x - 6y = 81

Now cross out the y's, because the +ve and -ve cancel eachother out, and then add the like terms of the x's and then the plain numbers:

x = (-26 + 81) = 55
Now substitute the new value of x into one of the original equations to find y:

5(55) - 2y = 27...275 - 2y = 27 (subtract 275 from both sides)

-2y = -248 (divide by -2 both sides)...y = 124

x = 55, y = 124

Answer 2

x+2y=-5 3x+3y=9 You'll want to get rid of either the x or y by making the coefficients equal. In this case, I'll make the x's equal, i.e. multiply the first equation by 3. Therefore: x(3)+2y(3)=-5(3) 3x + 6y = -15 Once we've done that, you can now get rid of the x but subtracting one equation from the other. (If one of the coefficients are a negative, you must add): 3x+6y =-15 - 3x+3y=9 --------------- 0 + 3y = -24 3y = -24 Now solve for y by making 'y' on it's own (i.e. get rid of the 3): 3y (/3) = -24 (/3) y = -8 You now have the value of -8. So to get the value of x, you can substitute y=-8 into one of the equations at the top. Therefore, when y=-8, x=... x+2y=-5 x+2(-8)=-5 x+-16=-5 x=11 Therefore, y=-8 and x=11

Answer 3

let 7x-3y=13 be eq 1
5x-2y=27 be equation 2

the idea is to eliminate either x or y in order to get x or y.

say if wanna eliminate x we will multiply eq 1 by 5 and eq 2 by 7

so now
eq 1 is 35x-15y=65
eq 2 is 35x-14y=189

now change the signs of each term in eq 2 so that 35x can be cancelled

once 35x is eliminated go on to solve equation to find y use y to find out x

Answer 4

ok...so I think this is how it goes...
7x-3y=13 (-2) you multiply all of this by -2 to get a positive 6y
5x-2y=27 (3) multiply all by 3 to get a -6y

-14x+6y=-26
10x-6y= 81 the +6 and -6 cancel out and = 0

-4x+0y(0)=55 => -4x=55

Then you divide -4 by 55 to get the x by itself

x=55/-4 => x= -13 3/4

Answer 5

take one of the equations and solve for x (or y) so you'd do
7x-3y=13
7x=13+3y
there for x=(13+3y)/7

take that and plug it into the other equation 5x-2y=27
good luck, i'm not sure if that is considered that elimination method or not, but that is how you could solve it.

Answer 6

Just don't eliminate all over your homework. Yuck.