Question

A system of equations is shown below:

3x + 8y = 12
2x + 2y = 3

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 1

@Mehek14

Answer 2

I can't really help with this cuz I suck at it

Answer 3

awww

Answer 4

yea sowwy :(

Answer 5

given 2 equations f and g

newf = f + kg, for some constant k

Answer 6

@amistre64 please explain that better :)

Answer 7

you have 2 equations defined, call one of them f and the other g

lets say g is a line: ax + by = c

multiplying by some constant k gets us

kg: kax + kby = kc

solve each for y

g: y = -ax/b + c/b
kg : y = -kax/kb + kc/kb , all the ks cancel top to bottom so the kg = g is the same line

Answer 8

Ok let me get this down :3

Answer 9

how to explain the sum of the equations of a set is also an equation equal to the set.

Answer 10

im still lost :( the way you word it makes me feel dumb

Answer 11

lets do this, well just follow the instructions ....

pick one of the equations

Answer 12

umm ax+bx=c

Answer 13

not quite what i meant, you posted 2 equations to play with, which pick one of them

Answer 14

2x+8y=12

Answer 15

now multiply it thru by some number, perferablly other than 0 or 1

Answer 16

umm i'll multiply 8 by 2?

Answer 17

lets say you want to use 2 as your multiplier

2(2x+8y = 12) --> 4x +16y = 24

Answer 18

ohhh

Answer 19

now add this new equation to the one you did NOT use.

this lag is something else isnt it ...

Answer 20

yes it is and 2x+2y(4x+16y) is that what you ment

Answer 21

you gave me an equation you did not post

you posted:

3x+8y=12
2x+2y=3

multiply one of them by some number, we did 2

2(3x+8y=12) --> 6x + 16y = 24

now add this to the other one

(6x+16y)+(2x+2y) = (24)+(3)

Answer 22

Ohhhh

Answer 23

27?

Answer 24

in general

spose we have 2 equations

a1x + b1y = c1
a2x + b2y = c2

added up we have

(a1+a2)x + (b1+b2)y = c1+c2

assume the solution set to the original 2 equations is (x1,y1)

then it is also a soluton to the sum of the equations
---------------------------

proof

a1 x1 + b1 y1 = c1
a2 x1 + b2 y1 = c2

substitute them into equation 3

(a1+a2)x1 + (b1+b2)y1 = a1 x1 + b1 y1 + a2 x1 + b2 y1

(a1+a2)x1 + (b1+b2)y1 = (a1 +a2)x1 + (b1 +b2)y1

QED

Answer 25

ok i do not understand that at all .-.

Answer 26

its just a general proof that the solution to a system of equations is also a solution to any linear combination of the set of equations

Answer 27

ahh
so am is that it for this question?

Answer 28

thtas the technical aspect of it yes, but the question is asking you to do something specific

we obtained a new equation that is the sum of the other equations

Answer 29

now we have to prove that the solution set to the first 2 is a solution to the one we created

Answer 30

ok can we hurry this up ccuz at in 50 minutes i must leave (even though i don'tthink it will take this long)

Answer 31

what is your solution set to the first 2 equations ?

Answer 32

first solution for the first equation is 27??

Answer 33

i havn't done the second equation

Answer 34

we dont have time to fight the lag and try to cover how to find a solution to the first set of equations

Answer 35

its assumed you know how to find the solution to the original setup to start with.

Answer 36

if all 3 equations are equal with the same set of (x,y) values then they share the same solutions

Answer 37

then their parallel lines

Answer 38

good lcuk

Answer 39

ok thanks