Question

Help Please !! Will Fan and Give Medals !!

A system of equations is shown below:
3x+8y=12
2x+2y=3
Part A:create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other.show the steps to do this.
Part B:show that the equivalent system has the same solution as the Original system of equations.

Answer 1

Have you considered multiplying the second by -4?

Answer 2

No I havent I really need help on learning how to do this..

Answer 3

Okay, multiply the second by -4.

Answer 4

Multiply 3 by -4?

Answer 5

2x+2y=3

Multiply by -4

-8x - 8y = -12

Answer 6

Does that become the overall equation..Im confused..Sorry..

Answer 7

\(\large \begin{array}{llll}
3x+8y=12&\to &\quad 3x\cancel{ +8y }=12\\
2x+2y=3&{\color{brown}{ \times -4}}\to &-8x\cancel{ -8y }=-12\\
\hline\\
&&\qquad \qquad ?
\end{array}\)

Answer 8

Would it be 3??:))

Answer 9

3? what do you mean?

Answer 10

The question Mark..Will the Overall answer be 3??:))

Answer 11

hmmm nope, is a sum
so you add the values vertically down
notice the variables are already lined up vertically

Answer 12

So the questions already answered thats all i needed to do..Can i ask a question?:)

Answer 13

sure

Answer 14

Were did you get the -4 from?? :))

Answer 15

is just an arbitrary value used to multiply one of the equations

Answer 16

what did the sum give you?

Answer 17

It gave me 3 :))

Answer 18

well... is not 3... notice there's a variable.... that you seem to be missing there

Answer 19

Ohhhh xD is the Missing Variable -4...is that what i was suppossed to find?

Answer 20

You are supposed to find values for x and y that make BOTH equations true simultaneously.

1) x+8y=12
2) 2x+2y=3

One method is called elimination.

Multiple 2) BY -4

1) x+8y=12
3) -8x-8y=-12

Add 1) and 3), combining like terms.

4) -7x = 0

Solve for x

5) x = 0

Substitute 5) into 1) to find the corresponding value for y.

6) 0+8y=12

Solve for y

7) y = 12/8 = 3/2

Check in 2)

8) 2(0)+2(3/2) = 0 + 3 = 3.

Done. The solution is (0,3/2). Perhaps it is more clear to write (x = 0, y = 3/2)

Answer 21

Thanks so verry Much @tKhunny:)) <3

Answer 22

Normally, I would insist that YOU do all the work. However, sometimes a discussion just drags on too long and I want to put a stop to it before someone becomes discouraged. Let's see you do one.