The Elimination Method?

Question

x-2y=2
3x-5y=7

Answer 1

The elimination method is designed to help you eliminate one variable entirely from the set of two equations.

x - 2y = 2
3x -5y =7

First thing you want to do is decide which variable you want to eliminate, by multiplying to make an opposite. In this case, it would be easier to eliminate x than y. If we were to eliminate y, we would have to multiply both equations to get 10y and -10y. It would be much easier to get 3x and - 3x.

Multipy the top equation by -3
-3x + 6y = -6
3x - 5y = 7

Add the columns.
y = 1.

Now that you have the y value you can substitute that value into one of the original equations to find the x value.
x -2(1) = 2
x - 2 = 2
x = 4.

y = 1, and x = 4

Check in the other equation.
3(4) -5(1) = 7
12 - 5 = 7
7 = 7

Left and right sides are equal so both values are correct.

Answer 2

You wanna make either the x or y cancel so I'll pick y.
(5) x-2y =2 (5)
(-2) 3x -5y= 7 (-2)

5x-10y=10
-6x+10y= -4
-1x = -4
divide.

x=4

Then pick one of the equations and plug 4 in for the x. I'll just pick the first equation.

4-2y=2
-4 -4

-2y=-2
Divide.
y= 1

The answer is: (4, 1)
Hope that helps. =)

Answer 3

multiply all of the top terms by -3, and then add the two equations
then plug the solution for y into the first equation
solve for x
put x and y solutions in a ordered pair