Solve the system using elimination. 6x-4y=28 7x+3y=2 What is the solution?

Question

 I do not understand anyone have the answer?

Answer 1

Hi Haylie!!

 

Using the system of elimination means that you need to eliminate one of the variables in order to solve for the other and then plug the found variable back in to one of the original equations to solve for the eliminated variable.

 

1) Write out the equations on top of one another.

7x+3y=2

6x-4y=28

 

2) You will be adding them together so Multiply both equations by different numbers that make either both x term or both y terms the same (I will do the y's)

4(7x+3y=2) = 28x+12y=8

3(6x-4y=28) = 18x-12y=84

 

3)Add the equations together (the y terms cancel out and leave only the x terms)

28x+12y=8

18x-12y=84

___________

46x+0=92

 

4)Solve for x

46x+0=92

46x=92

x=92/46

x=2

 

5)Now solve for y by plugging x back into either original equation!

7x+3y=2

7(2)+3y=2

14+3y=2  (subtract 14 from both sides)

3y= -12

y= -12/3

y= -4

 

(2,-4) Correct format for solution

 

You can plug x & y back into both original equations to check and see if these answers are correct. 

7(2)+3(-4)=2

14+-12=2

2=2 Correct!

 

6(2)-4(-4)=28  (don't forget that a negative times a negative equals a positive)

12+16=28

28=28 Correct!

 

Have a great day!!

Tiffany

 

Answer 2

6x - 4y = 28

7x + 3y = 2

 

The elimination method means that we multiply the equations by amounts where we can then remove a variable by adding/subtracting.

 

In your equations' case, you can multiply the first one by 3 and the second by 4. That will give us a -12y and 12y respectively that will cancel out:

3(6x - 4y = 28)
4(7x + 3y = 2)

 

18x - 12y = 84

28x + 12y = 8

-------------------

46x + 0y = 92

which becomes:

46x = 92

Divide both sides by 46:

x = 2

 

Now that we have x, we can solve and check for y:

6 * 2 - 4y = 28

12 - 4y = 28

-4y = 16

y = -4

 

(7 * 2) + (3 * -4) = 2

14 - 12 = 2

2 = 2