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# Systems of equations with substitution: y=4x-17.5 & y+2x=6.5

Learn to solve the system of equations y = 4x - 17.5 and y + 2x = 6.5 using substitution. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What if the problem is

-5x + y= -2

-3 + 6y= -12

How would I figure out either the x value first or the y value first ?
• You were already given the Y value, look:

-5x + y = -2 -3 + 6y = -12
y = -2 + 5x 6y = -9
y = -9/6
y = -3/2 <--- this is your Y value

Y = -9/3 (which is the same as -3/2), all you have to do to solve for X is substitute your Y value into the equation: -5x + 7 = -2

Here it goes:

-5x - 2/3 = -2
-5x = -2 +(2/3)
-5x = -4/3
x = (-4/3
• Are you supposed to use the substitution method whenever you see the systems of equations?
• Systems of equations can be solved by graphing, elimination, or substitution. Which one you use comes down to the systems of equations you're solving for, and how much work you want to do. Some systems solve easier using elimination, while others solve quickly using substitution.
• how would you solve this problem
x+y+7z=21
x+y+9z=29
x+y+4z=39
• If you subtract the first one from the second one, you find that z = 4.
If you subtract the third one from the second one, you find that z = -2.
So, those equations don't have a solution.
(1 vote)
• What's up guys
• the sky is up (or the roof)
• How does this apply to real life @_@
(1 vote)
• hi! sometimes, yes, you can't see why/how math applies to real life. and that is normal! you definitely may use it in the future, whether it be for your profession, or maybe financial purposes! either way, it is important. you also may need it for higher math classes, such as algebra. these are the fundamentals of math classes in your future.
• The problem is 840=(x+y) eq.1 & 840=(y-x)7 need to understand how to solve in substitution method HELP?
• how do i solve this
2x-3y=-24
x+6y=18
(1 vote)
• Try watching Sal's videos again before reading on.
Convert either of the equations into the form x = a*y + b or y = c*x + d
Substitute the value for x (or y) in the other equation
Solve this equation
Plug the result into either of the original equations
Solve that
Voila

So you could start by converting
x + 6y = 18
into
x = -6y + 18

Plug that into 2x - 3y = -24
2*(-6y + 18) - 3y = -24
Multiply into brackets
-12y + 36 - 3y = -24
Solve this equation for y
Plug the result into x = -6y + 18 to get x
• What would I do if there is a number in front of the y?
Like:
y=6x-11
-2x-3y=-7
What would y first step be?
Would the combined equation look like:
-2x-3(6x-11)=-7 ?
(1 vote)
• If you have
y=6x-11
-2x-3y=-7
and you want to solve by substitution, you can just substitute 6x-11 into the second equation everwhere you see a y
like this
-2x - 3(6x-11) = 7 Then distribute the -3 so
2x + ((-3)*6x) + ((-3)*(-11)) +33 = 7
-2x -18x +33 = 7

Does that help make it click for you.