Question

Solve the following system of equations using any method
3x+14y=−78
12x+12y=84

Answer 1

What do you think the solution is?

Answer 2

i have no clue, can you help?

Answer 3

Have you done simultaneous equations before?

Answer 4

i dont think so

Answer 5

Have you solved simple equations like 4x = 8?

Answer 6

yes

Answer 7

You'll be fine then.

Answer 8

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

Answer 9

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

Answer 10

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?

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

@lindsey_quick are you still with me?

Answer 16

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 ???

Answer 17

i got 5.57 and 7 ?

Answer 18

-56y = 312
12y = 84

What does -56y + 12y = ?

Answer 19

-44y

Answer 20

Correct!! Now what does 312 + 84 = ?

Answer 21

396

Answer 22

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?

Answer 23

9

Answer 24

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?

Answer 25

i think i got it from here , thanks

Answer 26

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!!!