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Question 251998: please help me solve: 2x-2y=4 and 3y-x=1
Found 2 solutions by Theo, MRperkins:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equations are:
2x - 2y = 4
3y - x = 1
presumably you want to solve them simultaneously.
use the second equation to solve for y in terms of x and then use that value to substitute in the first equation to solve for x.
second equation is:
3y - x = 1
add x to both sides and subtract 1 from both sides to get:
3y - 1 = x
take the value of x in terms of y and substitute in the first equation.
first equation is:
2x - 2y = 4
substitute 3y-1 for x to get:
2*(3y-1) - 2y = 4
simplify by performing indicated operatioons to get:
6y - 2 - 2y = 4
combine like terms to get:
4y - 2 = 4
add 2 to both sides of equation to get:
4y = 6
divide both sides of equation by 4 to get:
y = (6/4)
substitute for y in the second equation and solve for x.
second equation is:
3y - x = 1
replace y with (6/4) to get:
3*(6/4) - x = 1
simplify by performing indicated operations to get:
(18/4) - x = 1
add x to both sides of this equation and subtract 1 from both sides of this equation to get
(18/4) - 1 = x
simplify to get:
x = (14/4)
you have:
x = (14/4)
y = (6/4)
substitute in both equations to confirm these values will solve both equations (both equations will be true)
your equations are:
2x - 2y = 4
3y - x = 1
these equations becomes:
2*(14/4) - 2*(6/4) = 4
3*(6/4) - (14/4) = 1
simplifying, these equations become:
28/4 - 12/4 = 4
18/4 - 14/4 = 1
simplifying further, these equations become:
16/4 = 4
4/4 = 1
both these equations are true, so the values for x and y are good.
x = (14/4)
y = (6/4)
these answers are the same as:
x = 3.5
y = 1.5
Answer by MRperkins(300)  (Show Source):
You can put this solution on YOUR website! There are multiple ways to solve this system of equations. One method is to graph the two functions and find out where they intersect. Another method is to solve using substitution. A third method is to solve using elimination. A fourth method is to solve using a matrix, but I don't think that is the one you will be using right now.
The method of choice for this type of problem is elimination.
2x-2y=4
3y-x=1
Step 1, get the variables in the same columns (get x under x, y under y, constant(the number without a variable)under constant).
so
2x-2y=4
-x+3y=1
Step 2, multiply everything in one equation by a number that will allow one of the variables in that equation to be opposite the same variable in the other equation. In this example, we will multiply the second equation by 2 so that we get -2x (which is opposite 2x)
2(-x+3y=1)
distribute the 2
-2x+6y=2
Step 3, add the equations
2x-2y=4
-2x+6y=2
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0+4y=6
or y=3/2
now plug 3/2 in for y in one of the original equations and you get
2x-2(3/2)=4 Solve for x
2x-3=4
2x=7
x=7/2
so your solution is the point (x,y)=(7/2,3/2)
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Respectfully,
Justin
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