Solve the following systems of linear equations by elimination, showing all work: 3y+3x=-30 -2y+2x=-8help

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

To do elimination, you need to make it so that one of the variable terms will cancel itself out.  In other words, you need to be able to add two of one term together and get 0.

In this case, you can do this by making both one x term be 3x and the other be -3x..  The way to do that is to multiply the second equation by -1.5.

So then you would have the second equation being

3y - 3x = 12

Now you add the two equations together.  That gets you

6y = -18

Which makes y = -3 when you divide both sides by 6.

Now you plug this value of y into one of the equations to solve for x.  We'll do the second equation.

6 + 2x = -8

2x = -14

x = -7

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First of all, we have to take a look to the both equations, to see what unknown could be canceled. In our case, it is obviously that the unknown x could be canceled easier than y, because the coefficients of the unknown x have opposite signs.

After choosing what unknown could be canceled, we have to find out which is the common denominator of the coefficients of the unknown x. In this case is 2*3=6.

The next step is to multiply the first equation with 2 and the second equation with 3, after that the both equations will be added.

2(3y+3x) + 3(-2y+2x)=-60-24

6y+6x-6y+6x=-84

After reducing similar terms, we'll have:

12x=-84

x=-7

After finding the unknown x, we'll substitute it into what equation we choose.

3y+3x=-30

3y+3(-7)=-30

3y=-30+21

3y=-9

y=-3

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The given simultaneous linear equations are:

3y + 3x = - 30   ...   (1)

- 2y + 2x = - 8   ...   (2)

Multiplying equation (1) by 2 and equation (2) by 3 we get:

6y + 6x = - 60      ...   (3)

- 6y + 6x = - 24   ...   (4)

Adding equations (3) and (4) we get:

6y -6y + 6x + 6x = - 60 - 24

12x = - 84

Therefor x = -7

Substituting this value of x in equation (1) we get:

3y + 3*(-7) = - 30

3y - 21 = - 30

3y = - 30 + 21 = - 9

Therefor:

y = -9/3 = -3

Answer:

x = -7, and y = -3

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

3y+3x=-30...........(1)

-2y+2x=-8...........(2)

Both equations could be reduced. First by 3 and the second by 2.

(1) divided by 3 gives: y+x=-10..........(3)

(2)/2 gives:      -y+x= -4...................(4)

(3)+(4) gives: 2x= -14. Or x=-14/2 =-4.

(3)-(4) gives: 2y = -10--4 = -6. Or y = -6/2 = -3.

 

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