Question

solve the system of inequality
y=-x^2+2x-3
y=4x-3

Answer 1

Start with the first equation as shown in step 1. In step 2, you'll replace 'y' with '4x-3'. From then on, you get everything to one side and combine like terms.
\[\Large y=-x^2+2x-3\]
\[\Large 4x-3=-x^2+2x-3\]
\[\Large 4x-3+x^2-2x+3=0\]
\[\Large x^2+2x=0\]
I'll let you finish

Answer 2

wait so what do i do

Answer 3

hint: factor

Answer 4

im so confused

Answer 5

try to factor x^2+2x

Answer 6

how do i do that

Answer 7

what is the common factor of x^2 and 2x?

Answer 8

2?

Answer 9

am i right?

Answer 10

think of x^2 as x*x

Answer 11

what do x*x and 2*x have in common?

Answer 12

so x

Answer 13

right?

Answer 14

yes factor out x to get what?

Answer 15

1?

Answer 16

x*x+2*x = x*(....)

what goes in the parenthesis?

Answer 17

1

Answer 18

no

Answer 19

think of distribution but in reverse

Answer 20

wait what?

Answer 21

for example

x*(x+3) = x*x + 3*x = x^2+3x

so,

x^2+3x = x*(x+3)

Answer 22

okay now what

Answer 23

so what does x^2+2x factor to?

Answer 24

im not sure

Answer 25

use the example I posted

Answer 26

i still dont get it this is all so confusing to me im sorry

Answer 27

ok one moment

Answer 28

x times what will get you x^2?

Answer 29

x

Answer 30

x times what will give 2x?

Answer 31

2

Answer 32

so hopefully you can see how

x^2+2x = x*(x+2)

??

Answer 33

ok...?

Answer 34

if x*(x+2) = 0 then

x = 0
or
x+2 = 0 ----> x = ???

Answer 35

2?

Answer 36

x+2 = 0 leads to x = ???

it's not x = 2

Answer 37

1

Answer 38

no

Answer 39

SOMETHING plus 2 = 0

what is that SOMETHING

Answer 40

0

Answer 41

no

Answer 42

try to isolate x

Answer 43

this is making no sense i dont get it what can be added to 2 to make 0??

Answer 44

we have x+2 = 0

what must happen to both sides to move the 2 over?

Answer 45

subtract

Answer 46

subtract what

Answer 47

2

Answer 48

subtract 2 from both sides and you get what?

Answer 49

-2

Answer 50

ohhh -2+2=0

Answer 51

right?

Answer 52

yes so either x = 0 or x = -2

Answer 53

what about y?

Answer 54

if x = 0 then y=4x-3 = ???

Answer 55

y=4(0)-3

Answer 56

y=-3?

Answer 57

yes so (0,-3) is one ordered pair solution. There is one more ordered pair solution

Answer 58

if x = -2, then y=4x-3 = ???

Answer 59

y=4(-2)-3
-8-3
-11 y=-11

Answer 60

yep so the two solutions are `(0,-3)` and `(-2,-11)`

Answer 61

If you graph the two equations, the two curves will cross at (0,-3) and (-2,-11)

Answer 62

i dont need to graph but thank you so much!!

Answer 63

no problem