math question! help!?

Question

2y = 1 - 3x
3y = - (1+4x)
_______________
1/2x -1/5y = 1
y -1/3x=8
please show your work!

Answer 1

I assume they are two different problems.. but anyway:

You wanna use the elimination method:

(first, lets make the "Y's" equal each other to cancel out -
3 [2y = 1 - 3x]
2 [3y = -1 - 4x] (notice distributing the negative)

This is now:
6y = 3 - 9x
6y = -2 - 8x
Now subtract the equations from eachother
0 = 5 - x (notice subtracting negatives meant adding)
therefore x = 5, and "plug and check" means, y = -7
----------------------------------------------------------------------------
The 2nd problem is the same story:

1/2 x - 1/5 y = 1
y - 1/3 x = 8
Make the "X's" the same, let's not use fractions though so:
2 [1/2 x - 1/5 y = 1]
3 [y - 1/3 x = 8]
Giving us
x - 2/5 y = 2
-x + 3y = 24 (3y = 15/5 y)
This time we add the two together, not subtract:
13/5 y = 26
Therefore y = 10, x = 6

Answer 2

I assume they are two different problems.. but anyway:

You wanna use the elimination method:

(first, lets make the "Y's" equal each other to cancel out -
3 [2y = 1 - 3x]
2 [3y = -1 - 4x] (notice distributing the negative)

This is now:
6y = 3 - 9x
6y = -2 - 8x
Now subtract the equations from eachother
0 = 5 - x (notice subtracting negatives meant adding)
therefore x = 5, and "plug and check" means, y = -7
------------------------------...
The 2nd problem is the same story:

1/2 x - 1/5 y = 1
y - 1/3 x = 8
Make the "X's" the same, let's not use fractions though so:
2 [1/2 x - 1/5 y = 1]
3 [y - 1/3 x = 8]
Giving us
x - 2/5 y = 2
-x + 3y = 24 (3y = 15/5 y)
This time we add the two together, not subtract:
13/5 y = 26

there x=6 y=10

Answer 3

2y = 1 - 3x
3y = - (1+4x)

Now Multiply top with 3 and bottom equation with 2
6y = 3 - 9x
6y = -2 -8x
Now take top minus bottom equations
0 = 5 -x
x = 5, So put x = 5 into first equation
2y = 1 - 15
y = -7

Solution (5, -7)
_______________
1/2x -1/5y = 1
y -1/3x=8

Multiply 10 for top equation and 3 for bottom equation
5x - 2y = 10
3y - x = 24

Now put x = 3y - 24 from new second equation into new first equation
5 (3y - 24 ) - 2y = 10
15y - 120 - 2y = 10
13y = 130
y = 10, now put this into 3(10) - x = 24
x = 30 - 24 = 6
Solution is (6, 10)

Answer 4

Question 1
3x + 2y = 1-----------X by - 4
4x + 3y = - 1---------X by 3
-12x - 8y = - 4
12x + 9y = - 3--------ADD
y = - 7
4x - 21 = - 1
4x = 20
x = 5
Solution is x = 5, y = - 7

Question 2
5x - 2y = 10 (after X by 10)
- 5x + 15y = 120 (after X by 15)-----NOW ADD
13y = 130
y = 10
5x - 20 = 10
5x = 30
x = 6
Solution is x = 6, y = 10

Answer 5

and the slow way is

2y=1-3x
y = .5-1.5x

3y = -(1+4x)
3 (.5-1.5x) = -(1+4x)
-4.5x + 1.5 = -(1+4x)
4.5x - 1.5 = 1+4x
.5x - 1.5 = 1
x - 3 =2
x = 5

y = .5-1.5x
y = .5-1.5 (5)
y = .5-7.5
y = -7
__________________________________

y-1/3x=8
3y-x=24
-x=24-3y
x=3y-24

1/2x-1/5y=1
5x-2y=10
5(3y-24)-2y=10
15y-120-2y=10
13y-120=10
13y=120+10
13y=130
y=10

x=3y-24
x=3(10)-24
x=30-24
x=6