Question

MEDAL AND FAN DESPERATE... I JUST NEED TO KNOW HOW TO DO THE FIRST PROBLEM

Answer 1

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. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

Answer 2

the only reason why we would do part A is if we wanted to eliminate one of the variables in the process.

Answer 3

which variable do you think would be the 'simplest' to remove based on your own personal mathing skills.

Answer 4

x...

Answer 5

lol, either you are choosing x, or thats just some internet thing

Answer 6

lets say x can be removed ..... since -3 and -9 are multiples of each other, they share something in common, they can be easily modified for elimination

the y parts, 7 and 5 are mathically simple, but they require fractions and people are for some reason afraid of fractions.

Answer 7

-3x + 7y = -16
-9x + 5y = 16

we want to multiply the top by some number, k, such that we get a 9x to play with

-3kx = 9x when k=?

Answer 8

k=-3x/9x?

Answer 9

almost: divide by -3x :)

k = 9x/-3x = 3

Answer 10

@amistre64

Answer 11

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



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



9x + 21y = -48
-9x + 5y = 16

now we have a modified equivalent setup to play with. we are now able to elimiate the x parts to only deal with finding y

Answer 12

we add the two equations...correct?

Answer 13

yes

Answer 14

9x + 21y = -48
-9x + 5y = 16
16y= -32
16
y=-2

Answer 15

so, when y=-2, what does x equl?

Answer 16

and ... 21+5 = 26, not 16

Answer 17

26y = -32

y = -32/26 = -16/13

Answer 18

oddly enough, im getting 2 different answers :/

Answer 19

so does y equal-2?

Answer 20

-3x + 7y = -16
-9x + 5y = 16

got it ... i did (3) .. not (-3)

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

Answer 21

9x - 21y = 48
-9x + 5y = 16
--------------
0x -16y = 64

y = -4

Answer 22

foiled by a negative once again lol

Answer 23

by setting y=-4, we get x=-4 as a solution ... and part B says to see if this works in the original setup as well.