Question

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.

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

I'm really confused if anyone knows how to do this please help me!!!

Answer 1

I'm not actually sure about what they're asking us to do here, but if you're going to solve these equations like other simultaneous equations then we can do it like this:

Let's denote the equations like so:

(1) -3x+7y=-16
(2) -9x+5y=16

Then subtract 3 times (1) to 2 and we get:

-9x+5y-3(-3x+7y)=16-3(-16)
=> -9x+5y+9x-21y=16+48
=> -16y=64
=> y=-4

Sub y=-4 into (1) or (2):

-3x+7y=-16
=> -3x+7(-4)=-16
=> -3x-28=-16
=> -3x=12
=> x=-4

And there we have it: x=-4, y=-4. For B I think you just need to put these values of x and y back into (1) and (2).

Answer 2

Oh wow that makes so much sense now thank you so much!!!!!