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# Systems of equations with elimination: TV & DVD

Sal solves a word problem about the weights of TVs and DVDs by creating a system of equations and solving it. Created by Sal Khan and Monterey Institute for Technology and Education.

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• Why do you have to multiply the equation by -1? Can't you just subtract the 2nd from the first equation? It's much easier that way than multiplying the 2nd equation by -1 and adding it to the first equation.

Subtracting is the same thing as adding something negative.
• Yes that is completely true. You can definitely do that. But you see, the reason most people don't do this however is because it's very easy to forget which parts of the term should be negative or not; it's very easy to forget if a + or - sign should be assigned(it really depends on the person and how they do it). That's why people multiply by *-1* and then add, but you can definitely resort to just subtracting.
• sal says that 3t+2d is the same thing as 52, so, with that being said, can you divide 3t=52 and that giving you the answer for "t" and 52=2d giving you the answer for "d"?
• No. That doesn't work. You must have at least two equations to solve for two variables.
• anyone please do tell me the logic behind adding two equations to derive the unknown variables. is the logic similar to x + 1 =2 => x = 2 - 1 therefore, x=1 ?
• This is called collecting like terms and then isolating the variable x.
In your example we subtract both sides by 1 to isolate x on the other side alone.
• how would you solve the equation via substitution?
2x=5
x+y=7
• What you can do is x=5/2 because you want the x by itself then sub into equation #2 like this

Since we know x=5/2 we can do 5/2+y=7. no subtract 5/2 from both sides which will be:y=7-5/2=4.5
5/2=2.5
you can also check:
2(2.5)=5
2.5+4.5=7
• solving the system of linear equation by the addition method
{x+2y=7
{-x+3y=18
• When x = 3 and y = 5, by how much does the value of 3x2 – 2y exceed the value of 2x2 – 3y ? ineed answer and explanation plezzzzzz...
(1 vote)
• All you have to do is plug in the giving x and y values into both equations and solve.

I assume the 2 is an exponent on 3x2.
3(3)^2-2(5) = 17
2(3)^2-3(5) = 3

So it exceeds the value by 14.
• 6.5 is what percent of 9
• 72.2(the 2s go on forever)
• I am having trouble with this one : Given a word problem, how do you set it up in algebraic form and then solve it ?

Ten (10) years back, Jack’s father was four (4) times Jack’s age. But ten years from now, the father will be only 2 times Jack’s age. What are their current ages?
(1 vote)
• Always start with defining current ages, j for Jack and d for dad. So subtracting 10 gives f-10 = 4(j-10). Adding 10 years gives f+10 = 2(j+10). I assume you are okay with solving from here.
• how do I solve 3x+2y=-17
x-3y=9
• To solve a system of equations by elimination, you have to manipulate one or both of the equations so that when you add them together, one of the variables drops out.
3x + 2y = -17
1x - 3y = 9
If you were to multiply both sides of the second equation by -3, you would get:
3x + 2y = -17
-3x + 9y = -27
When you add the two equations together, you get:
0x + 11y = -44
or simply:
11y = -44
Divide both sides by 11 and you get:
y = -44/11 = -4
Now, substitute the value for y into either equation and solve for x:
x -3(-4) = 9
x -(-12) = 9
x + 12 = 9
x = 9 - 12 = -3
3(-3) + 2(-4) = -17
-9 + -8 = -17
-17 = -17
-3 - 3(-4) = 9
-3 + 12 = 9
9 = 9
Therefore: x=-3, and y=-4 is the solution to the system of equations.