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# Systems of equations with substitution: 9x+3y=15 & y-x=5

Learn to solve the system of equations 9x + 3y = 15 and y - x = 5 using substitution. Created by Sal Khan and Monterey Institute for Technology and Education.

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• i am told to solve each system using substitution .
how would i do this problem ?

m=2n
m+4n=30
• brian,

Your first equation, m=2n, is already solved for m in terms of n, so plug that in your second equation like this:

m=2n, so
m+4n=30 is the same thing as (2n)+4n=30

Therefore 6n=30, so n= 5. And if n=5 and m=2n, m= 2(5) =10.

Rechecking:
m+4n=30. If m=10 and n=5
(10)+4(5)=30
10+20=30
30=30. The answer m=10 and n=5 checks good.

This method is called solving by substitution, because you first solve for one variable in terms of the other using 1 equation, and then you substitute that solution in the other equation to solve for the second variable explicitly. Then you go back and solve for the first variable explicitly.

Does that help?
• no one's asked a question in 5+1 years.
Why is that?
• i dont even know becuase you said this 4 years ago
• I have watched almost all the videos for substitution and I still do not understand. For example, for the system of equations x=2y+7, and x=y+4, I got x=-6 and y=-3, but I'm not sure I'm right.
Plug the y in to find x
x = y + 4 = -3 + 4 = 1

Then plug them both in the other equation to check
x = 2y + 7 = 2(-3) + 7 = -6 + 7 = 1
• How do I solve -8x + y= -3
3x + 2y =13
I can't seem to find something similar.
• This problem can be solved using substitution. It takes a few more steps than simpler ones, but here's how you do it:
The first equations seems simpler, since the y has a coefficient (number before the variable) of 1. If we add -8x to both sides of the equation, we get y = 8x - 3. Now we can substitute this in for y in the second equation to get: 3x + 2(8x-3) = 13, and then we just solve for x. If you did the steps right, you should get x= 1. Then, by putting in 1 for x in any of the two equations, you should get y=5.
Let's check our work. -8(1)+(5) = -8+5 = -3, and 3(1)+2(5) = 3 + 10 = 13. This is right, so our solution set is x=1, y=5, or (1,5).
• how do i solve
y=x-6
y=2x-8
via substitution
• Since y = x-6 and y = 2x-8, set x-6 equal to 2x-8.
x-6 = 2x-8
-6 = x-8 Subtract x from both sides.
x = 2 Add 8 to both sides.

Plug in x for 2 into the first equation y = x-6: y = 2-6 = -4
Verify that the second equation y = 2x-8 holds true: y = 2(2)-8 = -4, -4 = -4!
• How do you solve this equation -3x-8y= 20 -5x + y=19
• is smth rong
• There are no errors at that time stamp. Why do you think something is wrong?
• Having trouble solving this
-4x+y=6
-5x-y=21
• Is 0/12 possible? What about 12/0? What's the difference?
(I am referencing in the video.)

And if two equations have the same y-intercept (b), does that make the system of equations' point to be that y-intercept point?
• 0/12 is 0. 12/0 is undefined. If you forget this, just ask yourself: "How many times does 12 go into 0?" Of course, this is not possible, so the answer is 0. 12/0, however, is undefined because 0 is basically nothing, and it is impossible to divide a number by 0. Hope this helps. -Grace
(1 vote)
• Hello,

At Sal starts graphing the slope as ''1 in the x direction and -3 in the y direction'' but later on counts it as ''2 in the x direction and -6 in the y direction.'' Why does he make this change and how do I know how to implement that when graphing?

Thank you,

- Fiona
(1 vote)
• To graph an equation you need at least two points. Sal found out that the Y-Intercept is is 5, and since the slope is is -3, Sal goes 1 in the X direction, and -3 in the Y Direction. Sal already has two points, so he can graph the line, but decides to find more points. So from that point, since the slope is -3, he goes 1 in the X direction again, and -3 in the Y direction again. Then he continues to do the same process one more time, but a bit differently. He goes down 6 in the Y Direction, and goes 2 to the right in the X direction.

Going 6 down in Y Direction and going 2 to the right in the X Direction, is the same thing as going down 3 in the Y Direction and going 1 to the right in the X Direction twice.

(-3) x (2) = -6
1 x 2 = 2

So you can see these two are equal.
Sal just saved some time for himself, and made the process a bit easier, by going down 6 and going to the right 2 instead of going down 3 and going to the right 1.

If your graphing by hand, you can do it either way, but it's usually more accurate if you only go one space in the X Direction. This also prevents silly mistakes from happening. However, if your experienced, you can go 2 in the X Direction, or 3 in the X Direction (or however many you want), as long as you multiply the distance you went in the X Direction by the slope.

I hope this helps.