Question

I will give anyone that helps me a medal

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.

Answer 1

\(\large \begin{array}{llll}
-3x + 7y = -16&{\color{red}{ \times -3}}\implies &\quad \cancel{9x}-21y=48\\
-9x + 5y = 16&&\cancel{-9x} + 5y = 16\\
\hline\\
&&\qquad\quad -16y=64
\end{array}\)

so, what do you think would "y" be if you were to solve for "y" there ?

Answer 2

-4?

Answer 3

yeap

now that you know what "y" is, you can just plug it on either equation, and solve for "x"
that's the so-called solving by ELIMINATION, we ELIMINATED the "x"
by using a multiple on one and then summing them up

Answer 4

Oh, thank you c:

Was that Part A or B?

Answer 5

well, part A asks to do as shown above

part B only says that you have to say, grab the RESULTANT equation from the sum
and check if the values are the same as the original equations

Answer 6

How do you do that? :o

Answer 7

hmmm lemme see if I get .. A.... .seems to ask for a yet another set

Answer 8

kk :3

Answer 9

.... the wording is a bit jumbled .... but basically is what was done

since you ended up with a new equation from the vertical SUM and a multiple of one of the equations

Answer 10

Ok, but how do I write down the steps? The end part got confusing :P

Answer 11

Oh, and how do I do Part B?

Answer 12

one could say that your original equations were
-3x + 7y = -16
-9x + 5y = 16

and after doing the ELIMINATION we had another one, a new one you can plug into the originals

so one could say that a new system of equations could be rewritten like
-3x + 7y = -16 or 0x -16y = 64
0x -16y = 64 -9x + 5y = 16

Answer 13

part B means, solve both systems
and see that the "x" and "y" on both are the same

so the new system per se, has the same solutions as the original system

Answer 14

Ooooooooooh, I get it :P, Thank you :3

Answer 15

yw