Question

A system of equations is shown below
5x - 5y = 10
3x - 2y = 2
Part A. Create and equivelant 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 equivelant system has the same solution as the original system of equations.

Answer 1

multiply the top eq by 2
multiply the bottom eq by 5

Answer 2

I'm still confused that doesn't exactly work

Answer 3

hmm so.. have you covered "system of equations" yet?

Answer 4

or... do you know how to solve a system of equations? have you covered either, substitution or elimination yet?

Answer 5

Kind of but it still just really confuses me

Answer 6

Can you explain to me how to solve the problem?

Answer 7

"equivelant system of equations by
replacing one equation with the
sum of that equation and
a multiple of the other"

so \(\large {
\begin{array}{rrrrrr}
5x - 5y = 10&\implies &5x - 5y = 10\\
3x - 2y = 2 &{\color{brown}{ \times \square }}&\implies
\square \cdot 3x+\square \cdot -2y=\square \cdot 10
\\\hline\\

\end{array}
}\)

so.. notice
you'd grab either, in this case, we use the 1st equation as is
and then
you grab the 2nd one and multiply times "something", you pick what value
then
sum them up vertically

and that'd give you a new equation, that you can use instead of either of the two original ones you had

Answer 8

say.. pick a value.... any value that we could use to multiply the 2nd one

Answer 9

I'm still not quite understanding sorry

Answer 10

2

Answer 11

ok.. so... let's start then by picking a value.. .ok so we'll use 2

Answer 12

Ok

Answer 13

\(\large {\begin{array}{crrcrrr}
5x - 5y = 10&&\implies &5x - 5y = 10\\
3x - 2y = 2 &{\color{brown}{ \times 2 }}&\implies &6x-4y=4
\\\hline\\
&&&\textit{sum them up}
\end{array}
}\)

notice.... you'd multiply, in this case the 2nd equation
by 2
then, sum up, the result from the multiplication, and the other equation

what would the sum give you?

Answer 14

But how do I find the values for the variables?

Answer 15

@jdoe0001

Answer 16

you'd sum them up vertically

Answer 17

What does that mean

Answer 18

hmmm well... you said you have solved system of equations already
so.... is the same as what you used in doing the "elimination" method

Answer 19

I have but I am not seeing how it relates

Answer 20

I'm really sorry this is just really confusing me

Answer 21

@jdoe0001

Answer 22

well... do you see the multiplication by 2 at least?

Answer 23

Yes

Answer 24

@jdoe0001

Answer 25

ok.. how about the sum? not obvious enough? \(\large {\begin{array}{crrcrrr}
5x - 5y = 10&&\implies &{\color{purple}{5x - 5y = 10 }}\\
3x - 2y = 2 &{\color{brown}{ \times 2 }}&\implies &{\color{purple}{ 6x-4y=4 }}
\\\hline\\
&&&\textit{sum them up}
\end{array} }\)

Answer 26

I understand that

Answer 27

ok... so... what would that sum give you though?

Answer 28

Are you asking me to multiply the top equation by 2 as well @jdoe0001

Answer 29

hmmm nope, to "sum them up"

Answer 30

How do I do that @jdoe0001

Answer 31

hmmm you may want to check your papers on the "elimination method"

that should cover sum of the equations vertically

Answer 32

II am in a quiz iso I can't otherwise I would

Answer 33

11x + 1y= 6?? @jdoe0001

Answer 34

I am not cheating this for something else not part of the quiz sorry if that was unclear

Answer 35

@pooja195