## anonymous one year ago Solve the following system of equations using any method 3x+14y=−78 12x+12y=84

1. anonymous

What do you think the solution is?

2. anonymous

i have no clue, can you help?

3. anonymous

Have you done simultaneous equations before?

4. anonymous

i dont think so

5. anonymous

Have you solved simple equations like 4x = 8?

6. anonymous

yes

7. anonymous

You'll be fine then.

8. jdoe0001

well... if you haven't covered "system of equations", how are you expected to solve it then?

9. jdoe0001

or using what "method" are you expected to solve it, that is, what chapter is this covering?

10. anonymous

What you need to do is simple, you just rearrange one of the equations so you have y or x on one side of the equation. Can you do that?

11. anonymous

Then I can take you through the next step after that.

12. anonymous

Lets solve for y first 3x+14y=−78 12x+12y=84 Times the top equation by -4 3x+14y=−78 -4(3x+14y)=−78 *-4 -12x - 56y= 312 Now you have a new equation and you can use the cancellation method to solve. Solve for y. Can you finish? -12x - 56y = 312 12x + 12y = 84

13. jdoe0001

if you haven't covered the material, I'd think this exercise doesn't apply to you then and your teacher should know better than to assign material he/she hasn't covered so... you may want to do that first

14. jdoe0001

can we do it for you? sure, do we know how to? yes does that help you? nope

15. anonymous

@lindsey_quick are you still with me?

16. anonymous

We have this now. -12x - 56y = 312 12x + 12y = 84 To solve for y we can use the cancellation method. -12x and 12x will cancel out because -12x + 12x = 0x = 0 so now we have the following equations -56y = 312 12y = 84 Can you finish solving for y ???

17. anonymous

i got 5.57 and 7 ?

18. anonymous

-56y = 312 12y = 84 What does -56y + 12y = ?

19. anonymous

-44y

20. anonymous

Correct!! Now what does 312 + 84 = ?

21. anonymous

396

22. anonymous

Correct!!! So -56y = 312 12y = 84 -56y + 12y = -44 and 312 + 84 = 396 so we have now -44y = 396 Now we need to get y by its self. since -44y is multiplication, we divide each side by - 44 $$\huge \frac{-44y}{-44} = \frac{396}{-44}$$ $$\huge y = \frac{396}{-44}$$ What do you get when you divide 396 by -44?

23. anonymous

9

24. anonymous

Close, you forgot your - symbol but yes -9. Ok we found our y value to the solution now to find the x value just put the y value into one of the original equation and solve for x. I am going to use 3x+14y=−78 3x+14(-9)=−78 Can you solve for x or do you still need a little help?

25. anonymous

i think i got it from here , thanks

26. anonymous

3x+14(-9)=−78 3x -126 = - 78 3x -126 + 126 = - 78 + 126 3x = -78 + 126 3x = 48 $$\huge \frac{3x}{3} = \frac{48}{3}$$ $$\huge x = \frac{48}{3}$$ $$\huge x = 16$$ So the solution is ( 16, -9) Good job! Practice makes perfect. Keep working at them and you will be a pro at them!!!