Question

MEDALLL

A system of equations is shown below:

5x - 5y = 10
3x - 2y = 2

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

multiply the second equation by 2 and add it to the first
then solve both systems

Answer 2

Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. <--- hint

Answer 3

@jdoe0001, that is what confuses me !

Answer 4

ok

so.. pick a multiple... any value, so we could use for one of them

Answer 5

well... I shoudln't say a "multiple"
pick an integer that is

Answer 6

2 ?

Answer 7

you'd, multiply, as cwrw238 pointed out, he's using a 2
you'd multiply one of them by some value
then
SUM that one and the other
to get a resultant equation

Answer 8

it could be any value, doesn't have to be 2
so... pick one

Answer 9

i'll do 2, but,
3x - 2y = 2
how would you do that ?

Answer 10

?

Answer 11

ok let us use 2 then
and let's multiply say the 2nd one
so \(\large {
\begin{array}{llll}
5x - 5y = 10&\implies &5x - 5y = 10\\
3x - 2y = 2&\implies {\color{brown}{ \times 2}}&6x-4y=4
\\\hline\\
&&\square ?\quad \square ?= \square
\end{array}
}\)

Answer 12

you would subtract the last things ?

Answer 13

well.. you'd add/subtract them both vertically
like you'd any values

Answer 14

so, it would be 11x - 9y = 14 ?

Answer 15

hmm lemme fix a typo there

Answer 16

thus \(\large {
\begin{array}{llll}
5x - 5y = 10&\implies &5x - 5y = 10\\
3x - 2y = 2&\implies {\color{brown}{ \times 2}}&6x-4y=4
\\\hline\\
&&{\color{blue}{ 11x -9y=14}}
\end{array}
\\ \quad \\

\begin{array}{llll}
5x - 5y = 10\\
3x - 2y = 2
\end{array}\quad \equiv\quad

\begin{array}{llll}
{\color{blue}{ 11x -9y=14}}\\
3x - 2y = 2
\end{array}\quad \equiv\quad

\begin{array}{llll}
5x - 5y = 10\\
{\color{blue}{ 11x -9y=14}}
\end{array}
}\)

Answer 17

part B
means you have to find "x" and "y"
in the original

and then find "x" and "y" in the new system of equations
to show that both match

Answer 18

so how do you do that?
plug in 0 ?

Answer 19

well... use substitutions or elimination
you'd sure have covered that

Answer 20

okay, thank you :)

Answer 21

yw