Question

Solve this system {4a-3b=-3
6a-b=6}

Answer 1

hello :) there's a few ways to solve systems of equations. which way are you most comfortable with? substitution method or elimination method?

Answer 2

right, there are 2 ways to solve this.

Answer 3

Um whichever way makes more sense. Im not really sure.

Answer 4

ok, well let's do the substitution method.

Answer 5

i'm going to use the second equation to solve for b

6a - b = 6
-b = -6a + 6
b = 6a - 6

Answer 6

gotcha

Answer 7

now i'm going to substitute that for b in the first equation

Answer 8

4a - 3b = -3
4a - 3(6a - 6) = -3
4a - 18a + 18 = -3
-14a + 18 = -3
-14a = -21
a = 1.5

Answer 9

now that we know what a equals, i'm going to substitute that in either equation

Answer 10

okay

Answer 11

6a - b = 6
6(1.5) - b = 6
9 - b = 6
-b = -3
b = 3

Answer 12

so our answer is a = 1.5, b = 3

Answer 13

make sense?

Answer 14

part b is)

Answer 15

thank you

Answer 16

c would not work

Answer 17

ok

Answer 18

you'd have multiply the second equation by -4

Answer 19

So its not C or D then

Answer 20

so A?

Answer 21

opps caught the "would not use"so its C

Answer 22

well it asks which method would \(\underline{not}\) work

Answer 23

gotcha sorry

Answer 24

exactly, so c is your answer

Answer 25

Could you help me with the next review problem? Please? Thanks!

Answer 26

yes, sorry. i was helping someone else

Answer 27

thats okay!

Answer 28

oh matrix... i haven't used that in forever :x lemme google it real quick for a refresher

Answer 29

lol ok

Answer 30

lol i think you might have to open a new question and get someone else to help with this. i'm sorry :/

Answer 31

it's been like a yr and a half since i used matrices

Answer 32

lol

Answer 33

okay, what about this one?

Answer 34

so long as i don't have to use matrices, i can help lol

Answer 35

ok lol

Answer 36

do you wanna use the substitution or elimination method

Answer 37

subsitution

Answer 38

alright. what should we do first, then?

Answer 39

use the second equation to solve the first one?

Answer 40

6a-6=b?

Answer 41

use the second equation to solve for b in terms of a

Answer 42

oops we already did this one. I meant {3x + 4y = 13
2x + y = 7}

Answer 43

oh lols. it felt familiar

Answer 44

ok! we're still going to use the second equation to solve for y in terms of x

Answer 45

y

Answer 46

*yes

Answer 47

2x + y = 7

subtract 2x from both sides
y = -2x + 7

Answer 48

yup

Answer 49

and now that we've solved for y, we're gonna substitute that for y in the first equation

Answer 50

ok

Answer 51

Sooo 3x + 4(7-2x) = 13

Answer 52

yes and now you can solve for x

Answer 53

x = 8/5?

Answer 54

3x + 4(7 - 2x) = 13
3x + 28 - 8x = 13
-5x + 28 = 13
-5x = -15
x = 3

Answer 55

Oh whoops okay

Answer 56

so now solve for y?

Answer 57

yep

Answer 58

9 + 4y = 13
4y = 4
y =1?

Answer 59

yes :)

Answer 60

so y = 1, x = 3

Answer 61

yea

Answer 62

What about this one?

Answer 63

?

Answer 64

i'm thinking

Answer 65

i'm not sure how to do it

Answer 66

ok

Answer 67

are there choices? if there are, you can just plug them in to each choice to see which one is true

Answer 68

nope there are no choices

Answer 69

what about this one?

Answer 70

wait i got the answer to that last one: a = 7, b = -2, c = 0

Answer 71

ok cool!

Answer 72

y = -12
x = 4

Answer 73

okay! what about this different problem?

Answer 74

@AriPotta

Answer 75

9?

Answer 76

How did you figure that out?

Answer 77

well i'm not 100% that it's correct

Answer 78

maybe it's -9

Answer 79

yea i think -9

Answer 80

3A + 5B = -12
-9A - 15B = 6

trying to solve with the elimination method, we'd have to multiply the first equation by 3, which would give us

9A + 15B = -36
-9A - 15B = 6

doing that would cancel both variables, so no solution

Answer 81

ok

Answer 82

what about this one?

Answer 83

ok so the slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. so first, we're going to find the slope by using the slope formula:\[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 84

then look at the graph to see what the y-intercept is

Answer 85

seeing a dotted line means it's going to be either < or >, not \[\le ~or~\ge \]

Answer 86

so have you figured out the slope?

Answer 87

um no i havnt. not sure how.

Answer 88

well it gives you two points, (0,2) and (-1,0), and i gave you the slope formula: \[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 89

oh right

Answer 90

2-0 / 0 - 1 = 2/-1

Answer 91

\[\frac{ 2-0 }{ 0-(-1) }=\frac{ 2 }{ 1 }=2\]

Answer 92

and, looking at the graph, what is the y-intercept?

Answer 93

um....not sure.

Answer 94

at which point does the line cross the y-axis?

Answer 95

ok so the y-intercept is (0,2). so so far we have y (< or >) 2x + 2