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# Systems of equations with elimination: x-4y=-18 & -x+3y=11

Sal solves the following system of equations by eliminating x: x-4y=-18 and -x+3y=11. Created by Sal Khan.

## Want to join the conversation?

• is this really the easiest way or can there be different ways??
• There are different ways, but this is most likely the simplest. But, the simplest may not always be the best way for you. ;)
• Now, what happens if you can't cancel out one of your variables? For example, 2x - 3y = 3, and 4x + 2y = 2. Then what?
• If you can't cancel one of your variable, you make it so that they can be canceled.
In your example, you would have to multiple 2x - 3y = 3 by -2
So, -2 (2x - 3y = 3)
After you multiply that, you would get -4x + 6y = -6
Now you are able to eliminate with 4x + 2y = 2
Now eliminate "4x" and add those equations together and you get 8y = -4
So, y = -1/2
Now that you know y, you can just plug it into any of the equations and get x
So, 4x + 2(-1/2) = 2
4x - 1 = 2
4x = 3
x = 3/4
• This whole thing is a bit KHAN-fusing (im not funny, for real, its hard.) can someone please help?
• Okay, this is a quick review with what the video was talking about in my point of view. I recommend you to write all this in your words on a notebook or sheet of paper.
Say you have two equations:
x-y=1
x+y=3
To do elimination the equations MUST be...
-aligned.
-in the same format.
-atop one another.
You also want ONE of the variables to be cancelled out/eliminated.
x-y=1 => We have a choice. We can either do addition
x+y=3 and have y eliminated, or do subtraction and
have x eliminated. Let's do addition.
x-y=1
+(x+y=3) => y is being cancelled out.
2x =4
x = 2 =>Nice! Now let's solve for y.

2-y=1 => Here, 2 is representing x. This time, we
-(2+y=3) to solve for y, so we cannot do addition
because addition will cancel y out. Let's
do subtraction.
-2y = -2
y = 1 => Huzzah! Joy is brought forth! The
solution is (2,1).

What Sal did was to multiply/divide each equation so they could be eliminated easily. Not all systems of equations can just go on and start eliminating. Sometimes, you need to multiply an equation so one of the values can eliminate the other.
Hope this helped. :)
• Can someone explain to me why this works? Sorry if it's a silly question.
• Elimination works because it eliminates one of the variables, we can solve the equation only if there is 1 variable and not 2 variables. This system of equation was super easy because you could eliminate the x variable right off the bat because x -x =0, so we cancel those two out and were left with just 1 variable in the equation, y, and then we can just solve it.

Basically, you manipulate the equations (multiplying both sides by a number, for instance) to cancel out one of the variables, leaving only 1 left, thus allowing you to solve for the variable left. Then you use that number and plug in back into one of the original equations to find the other variable you are looking for.

1 Eliminate one of the variables (doesn't matter which one)
2 Solve
3 Plug answer back into one of the original equations to find other variable
• Can anyone help me figure out how to do this equation 3x+8y=15
2x−8y=10?
i can't solve this without messing up.
• You're posting under the elimination method, so you'll want to find the least common multiple of either the coefficient of x or y. Then, you subtract the two equations to find the value of one variable. From there you substitute your now known variable to find the other unknown variable. I hope this helped!
• can you explain how to solve a system of equations with elimination? I need major help, I am pulling out my hair right now.
• According to Google, elimination is the complete removal or destruction of something. Therefore, you must multiply an equation by a certain number to eliminate a variable so that you're left with one variable. From there you can find out that one variable and substitute it back into the equation to find your other variable. I hope this helped!
• How many different ways to solve this?
• I think four: graphing, elimination, substitution, and matrices. All four are taught on Khan Academy, though matrices are a little higher level math than Algebra 1.
• I am working on a summer assignment and I have stumbled upon a problem that I do not understand, I am supposed to solve the systems of equations using elimination substitution and graphing. y1 = -3x+5 and y2 = 4x+12 the one and the two coefficient to the y's are tiny and I do not know their purpose nor do I know how to solve this problem please help explain it to me.
• The 1 and 2 subscripts really do not matter that much. This is asking you to find where the two equations intersect.
Elimination:
y= -3x+5
y=4x+12.
Let's eliminate y by subtracting equation 2 from equation 1.
=> 0= -7x-7
=> 7= -7x
=>x= -1.
Plug back in => y=8.
Substitution:
y= -3x+5.
y=4x+12.
Substitute y= -3x+5 into the second equation.
=> -3x+5=4x+12
=> 5=7x+12
=> 7x= -7
=> x= -1.
Plug back in => y=8.
Graphing the equations will show an intersection at (-1,8). So, all three ways give the same answer. In the future, you can use the one that you like.
• I get how to do it, but I don't understand why this works.
• this seems very simple, but I am having trouble with this:

Solve the system of equations:
-10y+9x=-9

10y+5x=-5

How would I solve for the x and y pair?