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# Systems of equations with elimination: x+2y=6 & 4x-2y=14

Learn to use elimination to solve the system of equations x + 2y = 6 and 4x - 2y = 14. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• how would i solve -14x+9y=46
14x-9y=102
• No solution means the lines are parallel... They will never cross.
• Hi I'm new to this topic so I am kind of confused in the first part. How do you know whether you add or subtract the two equations together.
(sorry if its a stupid question :)
• Here's an example. We have two equations, x+2y=6 and 4x-2y=14. Your question is how do we know whether you add or subtract the two equations together. Well, to know when to subtract or add the two equations, you want to know which variable to cancel out. Now what does that mean?

x+2y=6
4x-2y=14

As you can see in the second equation, it has the coefficient '2y' as the second term, right? Right now, its a negative term. In the first equation, '2y' is positive. Perfect. What is 2y -2y? It equals 0, or in other words, cancels out. Here's what it looks like.

1x+2y=6
+ 4x -2y = + 14 <-------- We add the equation to the first equation, but remember to subtract 2y.

This gives us 5x = 20, right? Right now, I'm going to assume you know how to solve the rest.
So lets recap, we add or subtract a variable to cancel out the other variable in elimination. If 4x-2y=14 was actually 4x+2y=14, and do what we did, it wouldn't cancel out the first equation.

To get it to cancel out 2y, we multiply the equation by (-1) by both sides.

-1(4x + 2y) = (14)-1
Turns into:
-4x -2y = -14

Do our magic.

x + 2y= 6
- 4x- 2y = -14 <--- Just solve and your done. We just need to cancel out one of the variables, x or y.

Ask any question if you still don't get it :)
• how do i solve these using elimination method?4x-5y=14;-4x-y=-6
• You add both equations together to get -6y=20, divide by -6 on both sides to get y=-10/3
• How do you know when to add or subtract?
• You can do either, its up to you, your preference. As long as you eliminate one of the variables.
(1 vote)
• 2x-y=8
3x+2y=20 (5,2)
• how to solve 4x+7y=-25 -12x-7y=19
• 7y and -7y are already opposites, so you can just add them together. You'll get -8x= -6. Solve for x, and then substitute and solve for y.
(1 vote)
• Can you use division to simplify an equation into elimination method structure? Example:
(6x-3y=15) / -3
2x+3y=-8
• Yes, the top equation just becomes -x=2x+y=-5
(1 vote)
• how would you solve using the addition method 3x+ 2y+18 and 2x-3y=-14