Question

Medal will be given!

A system of equations is shown below:

-3x + 7y = -16
-9x + 5y = 16

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. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

Answer 1

Btw, I think have have part A completed.

Answer 2

But I need help with part B, and need to make sure part A is done correctly.

Answer 3

multiply the 1st equation by -3 and then add the equations, this will eliminate x and allow you to solve for y

Answer 4

@campbell_st do you mean divide?

Answer 5

To eliminate x, shouldn't I preform the opposite operation?

Answer 6

well if you multiply the 1st equation by -3 you get and add the 2nd

9x - 21y = 48
-9x + 5y = 16
---------------
-16y = 64

Answer 7

So that's the correct answer for Part A? I thought it was

-3x + 7y = -16
-9x + 5y = 16

-9x + -3x = -12x

7y + 5y = 12y

-16 + 16 = 0

-12x + 12y = 0

Answer 8

But than again, I suck at math.

Answer 9

And I'm also a bit confused. Where did you get "9x - 21y = 48"?

Answer 10

I don't really understand the question.... to me... you are being asked to solve simultaneously

in doing so, y = -4 and x = -4

so you have the solution... so perhaps is

double the 1st equation and add the 2nd equation and you get

-6x + 14y =-32
-9x + 5y = 16
---------------
-15x + 19y = -16

so substituting the solutions x = -4 and y = -4

-15(-4) + 19(-4) = 60 - 76 = -16

so the solution of x = -4 and y = -4 is also a solution to the new equation that's been created.

Answer 11

So the sum of one of the equations is -4?

Answer 12

And if so, which one?

Answer 13

@campbell_st Wait, I think I get it now. Thank you so much! :)