Question

Solve using two different methods. Explain which method you found to be more efficient.
A. 3x-9y=3
6x-3y=-24

B. 7x-3y=20
5x+3y=16

C. y=1/2x-6
2x+6y=19

Please help me and show your work!! Thank you!
@agent0smith
@radar
@campbell_st
@helpme1.2
@bibby
@mebs

Answer 1

there's elimination method, subsitution, and for the really advanced yet super eay, matrix method

Answer 2

Okay, can we do elimination and matrix?

Answer 3

sure.. I wish draw would still work on here.. twiddla is the alternative

Answer 4

Okay..So how do I do it?

Answer 5

http://www.twiddla.com/1470390 draw the problems ... equations from here

Answer 6

We are going to work through twiddla?

Answer 7

@agent0smith can you help me?

Answer 8

sorry I was kind of busy with my own probz... but I did solve the first one through matrix on twiddla

Answer 9

I don't see it

Answer 10

http://www.twiddla.com/1470390

Answer 11

zoom out

Answer 12

control - to zoom out

Answer 13

I don't understand that! I am sorry, but it looks like a bunch of gibberish. Can you make some kind of chart here?

Answer 14

os isn't working too well for me at the moment

Answer 15

I need someone who can help me do these problems, @UsukiDoll is there anyway that you can make a chart on anything to help me see it?

Answer 16

I don't think I could if os is messing with me at the moment. :(

Answer 17

Can anyone help me?

Answer 18

SUBSTITUTION :
3x - 9y = 3 (when dividing by 3, reduces to x - 3y = 1)
x - 3y = 1 --add 3y to both sides
x = 3y + 1
now we can use substitution. Sub in 3y + 1 in for x in the other equation
6x - 3y = -24
6(3y + 1) - 3y = -24 -- distribute through the parenthesis
18y + 6 - 3y = -24 -- subtract 6 from both sides
18y - 3y = -24 - 6 -- combine like terms
15y = - 30 -- divide both sides by 15
y = -30/15
y = -2
now sub -2 in for y in either of the equations to find x
3x - 9y = 3
3x - 9(-2) = 3
3x + 18 = 3
3x = 3 - 18
3x = - 15
x = -15/3
x = -5
solution is (-5,-2)
ELIMINATION :
3x - 9y = 3 --->(-2)
6x - 3y = -24
----------------
-6x + 18y = -6 (result of multiplying by -2)
6x - 3y = -24
----------------add
15y = -30 -- divide by 15
y = -30/15
y = -2
now sub -2 in for y in either of the equations to find x
6x - 3y = -24
6x - 3(-2) = -24
6x + 6 = -24
6x = -24 - 6
6x = -30
x = -30/6
x = -5
Solution is (-5,-2)
========================
ELIMINATION :
7x - 3y = 20
5x + 3y = 16
--------------add
12x = 36 -- divide by 12
x = 36/12
x = 3
now sub 3 in for x in either of the equations to find y
7x - 3y = 20
7(3) - 3y = 20
21 - 3y = 20
-3y = 20 - 21
-3y = -1
y = 1/3
check..
5x + 3y = 16
5(3) + 3(1/3) = 16
15 + 1 = 16
16 = 16 (correct)
solution is (3,1/3)
SUBSTITUTION :
7x - 3y = 20
7x = 3y + 20
x = 3/7y + 20/7
now sub 3/7y + 20/7 in for x in the other equation to find y
5x + 3y = 16
5(3/7y + 20/7) + 3y = 16
15/7y + 100/7 + 3y = 16 -- multiply entire equation by 7
15y + 100 + 21y = 112 -- subtract 100 from both sides
15y + 21y = 112 - 100
36y = 12 -- divide by 36
y = 12/36
y = 1/3
now sub 1/3 in for y in either of the equations to find x
7x - 3y = 20
7x - 3(1/3) = 20
7x - 1 = 20
7x = 20 + 1
7x = 21
x = 21/7
x = 3
Solution is (3, 1/3)
=====================
SUBSTITUTION :
y = 1/2x - 6
now sub 1/2x - 6 in for y in the other equation
2x + 6y = 19
2x + 6(1/2x - 6) = 19 -- distribute through the parenthesis
2x + 3x - 36 = 19 -- add 36 to both sides
2x + 3x = 19 + 36 -- combine like terms
5x = 55
x = 55/5
x = 11
now sub 11 in for x in either of the equations to find y
y = 1/2x - 6
y = 1/2(11) - 6
y = 11/2 - 6 --- common denominator is 2
y = 11/2 - 12/2
y = -1/2
solution is (11,-1/2)
ELIMINATION :
y = 1/2x - 6 -- subtract 1/2x from both sides
-1/2x + y = -6 --- multiply by -1 to make x positive
1/2x - y = 6
now we have :
1/2x - y = 6 --->(-4)
2x + 6y = 19
--------------
-2x + 4y = -24 (result of multiplying by -4)
2x + 6y = 19
-------------add
10y = - 5
y = -5/10
y = -1/2
now sub -1/2 in for y in either of the equations to find x
2x + 6y = 19
2x + 6(-1/2) = 19
2x - 3 = 19
2x = 19 + 3
2x = 22
x = 22/2
x = 11
solution is (11,-1/2)