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How do you solve 3x+y =-2 and x-y=6?

With whatever method is easiest...substitution or elimination?

5 Answers by Expert Tutors

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Kiana V. | Let's Develop Your Math and Art Skills!Let's Develop Your Math and Art Skills!
5.0 5.0 (8 lesson ratings) (8)
1

You can also cancel -y and +y just by adding this two equations. so when you add it just left with:

4x=4

x=1 

then plug back 1 to one of the equation.

1-y=6

1-6=y

y=-5

Margery B. | Your best bet for Graphic Design!!Your best bet for Graphic Design!!
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I would solve for x with the first equation, then use that to solve for y in the second, then check by inputting values.

3x+y=-2
x-y=6
x=6+y

then...

3(6+y)+y=-2
18+3y+y=-2
18+4y=-2
4y=-20
y=-5

So..

3x+-5=-2
3x=3
x=1

3(1) + -5 = -2  ... yes! :)

Andy L. | Polymath College Tutor Specialize in The Liberal Arts and SciencesPolymath College Tutor Specialize in The...
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In this scenario, the goal of finding the values of both x and y the fastest is to find which variable will be easiest to solve and determine its values, which in this case must be x because you can use elimination or substitution to derive at x.
 
Elimination Process:
3x+y=2 and x-y=6 (adding them together)
4x=8 --> x=2
2-y=6 --> (through common sense) y=-4 since 2-(-4)=2+4=6
Test the solution witht he other equation:
3(2)+(-4)=6-4=2
 
Substitution Method: (as written above margery b.)
 
The key here Angelica is to use your instinct and determine what variable is best to be eliminated first so that you are left with only one variable to solve.
 
If you need any further help on your math, please check my profile or shoot me another email for tons of mathematical magics.
 
-Andy Lai "If adversary smiles, military people smiles back"

Comments

Andy,
 
Your method is perfect but the 1st equation is 3x+y=-2 not 3x+y=2.
Johnny R. | Exceptional Math and Accounting TutorExceptional Math and Accounting Tutor
4.8 4.8 (162 lesson ratings) (162)
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This is a system of linear equations that can be solved by elimination and substitution: First we will use elimination to solve for x 3x + y = -2 x- y= 6 Add the 2 equations and the result is: 3x + y = -2 x- y= 6 4x = 4 Divide both sides by 4 (Inverse operation) 4x/4 = 4/4 x= 1 Substitute 1 for x in the 1st equation 3 (1) + y = -2 3 + y = -2 Subtract 3 from both sides (Inverse operation) 3-3 +y = -2 - 3 y = -2 + -3 y = -5 Substitute the solution for x and y into both equations to verify. 3(1) + -5 = -2 3 + -5 = -2 -2 = -2 1-(-5) = 6 1+5 = 6 6=6

Danielle S. | Math - Various, Spanish 1 and 2, Powerpoint, Basic artMath - Various, Spanish 1 and 2, Powerpo...
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SO the first answer is Substitution and the Second answer offered is using Elimination.  I would say in this case the Elimination is easier, but both are quite simple for this problem.

Comments

I prefer Elimination myself although the beauty of math allows more than one method with the same result.  Please note that Andy's answer is only different because he had the 1st equation wrong.