Question

Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Answer 1

This is what i have so far.:
2. A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
a. Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
2 x 3 + 7 x 3 = 3
6x + 21y = 3
+-3x -4y +5
3x + 17y = 8
b. Use any method to solve the equivalent system of equations (the new first equation with the original second equation). I used the substitution method and substituted x and y for 3.
c. Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Answer 2

only part C confuses me...

Answer 3

lemme get this straight,
these are the "orginal system"
2x + 7y = 1
-3x – 4y = 5

and the "equivalent system" is...?

Answer 4

when you have a solution, plug it into the original setup ....

Answer 5

yes..the equivalent equation is:
3x + 17y = 8

Answer 6

in order to see if x=7 is a solution to 3x=21 ... plug it in

in order to show that a solution of one thing is also a solution to another .... plug em in

Answer 7

So how do i solve part c?

Answer 8

@DemolisionWolf @amistre64

Answer 9

what is the solution to the equivalent eqauation?

Answer 10

C is simply stating ... check to make sure youre solution works.

Answer 11

A - Use an equivalent system
B - Solve the equivalent system
C - Make sure the solution works in the original setup.

Since you already have the solutions form B, .... see if they work

Answer 12

i used 3 to find my equivalent equation so i have to divide them all by 3 to see if it gives me my original equations solution?

Answer 13

2x + 7y = 1
-3x – 4y = 5


redo step A for me ... i cant read what youve posted. It looks like equation 1 was multiplied by 3; but what did you to to equation 2?

Answer 14

Nothing...was i supposed to do something to it?

Answer 15

dunno, these instructions are a bit looney

Multiply the first equation ...

2x + 7y = 1
6x + 21y = 3

and add it to the second equations

6x + 21y = 3
-3x – 4y = 5
--------------
3x + 17y = 8


now we have an equivalent setup

6x + 21y = 3
3x + 17y = 8

which it says to solve by your favorite method .... which seems like an awful lot of extra work to me

Answer 16

if we eliminate, multiply the bottom by -2

6x + 21y = 3
-6x -34y = -16
----------------
-13y = -13

y = 1

replace y by 1

6x + 21(1) = 3

solve for x

6x = -18 ; x = -3

so, is x=-3, and y=1 a solution to the original setup of

2x + 7y = 1
6x + 21y = 3

Answer 17

ohh ok...makes sense.

Answer 18

copied the wrong "original" ...

2x + 7y = 1
-3x – 4y = 5

see if they work in that setup .... also known as double checking your results

Answer 19

thank you for your trouble :)

Answer 20

wait what is the answer to c?!?!

Answer 21

@undeadknight26

Answer 22

this isnt a free answering service .... what about the process did you not get?