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# Systems of equations with elimination: 3t+4g=6 & -6t+g=6

Sal solves the system of equations 3t + 4g = 6 and -6t + g = 6 using elimination. Created by Sal Khan and Monterey Institute for Technology and Education.

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• Hi would it also work if you multiplied the bottom equation by negative 4 to get the g's to cancel out? Thanks
• That is exactly what I was thinking. Yes that would definitely work.
(1 vote)
• In the :50-:57 range in the video, you decided to multiply by twos? My "teacher" says the same thing, to multiply by [ a random number]. I don't get it. How do you decide what to multiply the equation by?
(1 vote)
• You decide by recognizing what number you'll need to cancel the two terms.
In this video Sal recognized that the '3t' term could be multiplied by '2' to get a '6t'. That '6t' would then cancel with the '-6t' of the other equation.
It's really no more complicated than that. If his two terms happened to have been '3t' and '-9t', then he would have simply decided to multiply by '3'. That way '3t' would become '9t' which would cancel with the '-9t'.
• Um. Is it just me or is the equations solved a little too quickly for people to take notes? Could it maybe be slowed down a notch?
• how would you do an equation such as x+y=2
x-y=4
• i sure it would be
x+y
+
x-y for substitution not elimination
(1 vote)
• Hi this site is very useful. but i have a certain equation that your videos isn't answering. it is Y=-3x+5 and Y=-4x-1 and i Have to solve it by elimination. please help
(1 vote)
• y = -3x+5
y = -4x-1
You said elimination? So first we eliminate a variable. It looks like y has the same coefficient in both equations, so we can just subtract these two equations and the two y's will cancel out.
y = -3x+5
-(y= -4x-1)
0=x+6
We subtract 6 from both sides.
x=-6
Put it back into the equation.
y = -3x+5
y = -3(-6)+5
y= 18+5
y = 23
Hope that helped!
• I have watched this video twice now and still don't understand how to do these.
• The use of elimination is based on a number and its opposite adding to be zero
In the problem 3t +4g = 6 and -6t +g=6 has nothing to eliminate until you realize that 3*2=6, so if I multiply the first equation by 2, I will have a 6t and its opposite -6t which add to zero
2(3t+4g=6) use distribution to get
6t + 8g = 12 Line up second equation under this
-6t + g = 6 If I simple "add" these equations, 6t and -6t make zero
9g = 18 Divide both sides by 9
g = 2 Substitute for g in either equation
3t + 4(2) = 6
3t + 8 = 6 Subtract 8 on both sides
3t = -2 Divide by 3
t = -2/3 and from previous g = 2

This is easy to check by substituting both answers into the other equation you have
-6(-2/3) + 2 = 6 ( 12/3 + 2 = 4+2 =6) so we see that 6=6 and confirm we have right answer

Hope this helps
• Made up problem: 7x - 2y = 84
3x - 0.857y = 36

Is it possible to first multiply the lower equation by seven, then divide by three? In other words: can you multiply and divide one equation until you can find something that's equivalent to the other equation?
• As long as you do it right you can manipulate an equation which way you like, but generally you want to avoid doing unnecessary steps as it is time consuming. If one method requires a lot of steps, you could consider using another method for that problem (ex. substitution in this case).

Short answer: yes, you can :)
• anyone know how to get black hole badges
(1 vote)
• Solve the system of equations using elimination
A mathematician turned farmer has cows and chickens. He tells you that among the cows and chickens, there are 148 legs and 60 heads. How many cows and chickens are on his farm?
(1 vote)
• x= cow
y= chicken
4x + 2x= 148 (the four comes from the number of legs that cows have, and the two comes from the number of legs chicken have which total 148)
x+y= 60 (cause both just have one head)
Now to solve by elimination you set either the x or the y to the second equation so that they cancel out. ill just do it with the y. so multiply x+y=60 by -2 so that when you add, the y's will cancel.
4x+2y=148