Question

Help please Solve the system of equation by elimination and substitution
-66x-5y=-24
11x+4y=-21

Answer 1

What do you already know to do?

Answer 2

I did the problem i just ended up with a fraction so i don't know if its right

Answer 3

fractions can do that. Show me a few of your steps

Answer 4

the objective of this method is to make the coefficient of one variable equal and opposite so when the equations are added that variable is eliminated. you are left with a linear equation. solve for that variable then use the value in either of the expressions to solve for the eliminated variable. It is a very good practice to check your solution in either of the originals

Answer 5

This is what i did
-66x-5y=-24
11x+4y=-21 i multiplied the second equation by 6 to cancel out x

so it would look like -5y=-24
24y=-126

Answer 6

yep

Answer 7

then i got -19=-150/-19

Answer 8

y*

Answer 9

when you solve a system of equations it means you are finding the (x,y) that will satisfy both equations at the same time

Answer 10

24v + -5y = 19y

so y = -150/19

Answer 11

it's ugly, but the math is correct

Answer 12

i know i have to find the value of (x,y) that will work in both equations

Answer 13

I was just working on graphing this and i didnt get the same answer thats my main problem

Answer 14

What have you tried to eliminate y?

Answer 15

when you solve a system of equations it means you are finding the (x,y) that will satisfy both equations at the same time

Answer 16

i tell you the solution i got

Answer 17

I would not recommend trying to find a solution by graphing...! Your first approach was fine, you did the calculations right. It's just an awkward answer

Answer 18

go ahead

Answer 19

y=-150/19 x= 201/209

Answer 20

and its a project so i sorta have to do it :/

Answer 21

oof. Use really big graph paper...

Answer 22

But for substitution can you help me?

Answer 23

your solution is correct

Answer 24

i have to show it in the substitution method

Answer 25

where do you think you should start with substitution?

Answer 26

isolate one of the variables

Answer 27

okay, pick one

Answer 28

x

Answer 29

first or second equation?

Answer 30

what do you recommend :/

Answer 31

If nothing jumps out at you, which ever looks less complicated

Answer 32

2nd

Answer 33

okay - so for now forget about the first equation, and simply solve for x

Answer 34

y must be 0 right?

Answer 35

no, just get x by itself

Answer 36

i could add 5 y to -24

Answer 37

i mean -21

Answer 38

forget about the first equation... just focus on the second

11x+4y = -21

solve for x

Answer 39

is that what you were doing?

Answer 40

yeah but i substituted y for 0

Answer 41

youre thinking about intercepts

Answer 42

get x by itself

Answer 43

you got this...

Answer 44

ok 11x+4y=-21
-11 -11
x+4y=-10

Answer 45

....

Answer 46

right idea, wrong numbers...

Answer 47

so 4?

Answer 48

you are indeed subtracting soemthing from both sides, but not 11x

Answer 49

just 4?

Answer 50

4y

Answer 51

bingo

Answer 52

so now you have 11x = -21 - 4y

Answer 53

so 11x+4y=-21
-4y -4y
11x= -21- 4y

Answer 54

Now i remember lol

Answer 55

correct. what's next?

Answer 56

:)

Answer 57

substitute that into the other equation

Answer 58

almost. one more step to solve for x first

Answer 59

it isn't quite by itself yet...

Answer 60

how would i get rid of y?

Answer 61

you have 11x = -21-4y. You want "x = blah blah blah" What needs to be done so there is no "11"?

Answer 62

oh so y can remain so i can subtract 11 from -21 making it x=-31+4y

Answer 63

closer still... you can only subtract 11 if it's being added. It is not. It is being multiplied to x. So to undo that you must_______ by 11

Answer 64

add

Answer 65

sorry

Answer 66

no worries

Answer 67

so now substitute?

Answer 68

-66(-10+4y)-5y=-24 ?

Answer 69

you are so close. You have the substitution correct

Answer 70

You're just missing one thing on your solution for x

Here's a simpler example:

2x + y = 5
2x = 5 - y
x = (5-y) /2

Answer 71

...

Answer 72

So what exactly did i do wrong

Answer 73

11x = -21-4y

divide both sides by 11

Answer 74

x = (-12-4y)/11

Answer 75

er... -21

Answer 76

So adding could'nt be effective?

Answer 77

no, because we aren't adding or subtracting 11 and x. we are multiplying 11 by x. So the only way to eliminate the 11 is to divide it

Answer 78

Ok I'll revise the equation

Answer 79

yea, your substitution was spot on except for the dividing by 11 part

Answer 80

-66(-12-4y/11)-5y=-24

Answer 81

correct. and yuck. what a mess.

Answer 82

I know right

Answer 83

Now distribute -66 right

Answer 84

yes...

Answer 85

let me see what you have after that, I want to give you some advice, but I don't want to interupt your train of thought. you're doing great

Answer 86

792+264y/11-5y=-24

Answer 87

do i distribute 11 too?

Answer 88

no, because it isn't outside any parenthesis

Answer 89

Oh ok

Answer 90

just checking if i was correct

Answer 91

however, this is wehre the advice comes in. It would be much easier to deal with this if it werent for that fraction

Answer 92

so would we multiply now to get rid of it

Answer 93

yes!

Answer 94

becareful about how you do it tho

Answer 95

\[\frac{ 792+ 264y}{ 11 } -5y=-24\]

Answer 96

you have to multiply every term by 11

Answer 97

i thpought it was only on each side

Answer 98

thought*