Solving systems of equations?

Question

solve the following systems of equation by elimination

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

2. 3x + 7y = -6
x - 2y = 11

3. 5/x + 3/y = 4
25/x - 2/y = 3

with solutions. thanks.

Answer 1

5x - 2y = 3- - - - - - Equation 1
y = 2x- - - - - - - - - -Equation 2
- - - - - - - - -
Insert the y value equation 1 into equation 2

5x - 2y = 3

5x - 2(2x) = 3

5x - (4x) = 3

5x - 4x = 3

x = 3

Insert the x value into equation 2
- - - - - - - -
y = 2x

y = 2(3)

y = 6

Insert the y value into equation 2
- - - - - - - - -

Check for equation 2

y = 2x

6 = 2(3)

6 = 6

- - - - - - - --

Check for equation 1

5x - 2y = 2

5(3) - 2(6) = 3

15 - 12 = 3

3 = 3

- - - - - - - -

Both equations balance

The solution set is { 3, 6 }

- - - - - - - - - -s-

Answer 2

1)
5x - 2y = 3 ...............(1)
y = 2x.........................(2)
from (2) 2y - 4x = 0...(3)

(1) + (3) => x = 3

=> from (2) y = 6

2) 3x + 7y = -6 ..................(1)
x - 2y = 11 .....................(2)
from (2) 3x - 6y = 33 .....(3)
(1) - (3) => 13y = -39 => y = -3
=> x = 11 - 6 = 5

3) 5/x + 3/y = 4..............(1)
25/x -2/y = 3...............(2)
5*(1) => 25/x + 15/y = 20...............(3)
(2) - (3) => -17/y = -17 => y = 1
=>5/x + 3 = 4
=> 5/x = 1 => x = 5

Answer 3

1)
5x - 2y = 3 (eq. 1)
y = 2x (eq. 2)
_______________
Multiply eq. 2 by 2
2(y = 2x) =
2y = 4x (eq. 3)
Add eq. 1 and eq. 3
5x - 2y = 3 (eq. 1)
+ (2y = 4x)
_____________
5x = 3 + 4x
5x - 4x = 3
x = 3
Subtitute the value of x in eq. 2 to find y
y = 2x (eq. 2)
y = 2(3)
y = 6
===========================
2)
3x + 7y = -6 (eq. 1)
x - 2y = 11 (eq. 2)
Multiply eq. 2 by -3
-3(x - 2y = 11) (eq. 2)
-3x + 6y = -33 (eq. 3)
Add eq. 1 and eq. 3
3x + 7y = -6 (eq. 1)
+ (-3x + 6y = -33) (eq. 3)
____________________
13y = -39
y = -39/13
y = -3
Substitute the value of y into eq. 2 to find x
x - 2y = 11 (eq. 2)
x - 2(-3) = 11
x + 6 = 11
x = 11 - 6
x = 5
==========================
3)
5/x + 3/y = 4 (eq. 1)
25/x - 2/y = 3 (eq. 2)
Multiply eq. 1 by -5
-5(5/x + 3/y = 4) (eq. 1)
-25/x - 15/y = -20 (eq. 3)
Add eq. 2 and eq. 3
25/x - 2/y = 3 (eq. 2)
+ (-25/x - 15/y = -20 (eq. 3)
_________________________
-17/y = -17
-17y = -17
y = -17/-17
y = 1
Substitute the value of y in eq. 1 to find x
5/x + 3/y = 4 (eq. 1)
5/x + 3/1 = 4
5/x + 3 = 4
5/x = 4 - 3
5/x = 1
x = 5

Answer 4

1. 5x- 2y=3---(1)
y=2x---(2)
multiply (2) by 2
2y=4x---(3)
(1)+(3) gives
5x-2y=3
-4x+2y=0
--------------
x=3
therefore,y=2*3=6

2.
3x+7y=-6----(1)
x-2y=11-----(2)
multiply (2) by 3
3x-6y=33---(3)

(1)-(3) gives
3x+7y=-6
3x-6y=33
--------------
13y=-39
y= -3
therefore,x=11+2y=11-6
X=5

3.
5/x + 3/y= 4--(1)
25/x- 2y=3--(2)
multiply (1) by 5,we have
25/x+15/y=20--(3)
(3)-(2) gives
17/y=17
therefore,y=1
substituiting in (1),
5/x+3=4
5/x=1
x=5

Answer 5

haha, you're quite lazy actually

1. Subst. y=2x
5x-2(2X) =3
x=3, y=6

2. 3x+7y=-6 -----(1)
x - 2y = 11 -----(2)

2 X 3: 3x - 6y = 33 ------(3)

(1)-(3): 13y=-39
y=-13

3. 3. 5/x + 3/y = 4 -----(1)
25/x - 2/y = 3------(2)

(1) X5: 25/x+15/y=20 -----(3)

(3) -(2): 17/y=17
y= 1
subst. back to (1)
5/x +3=4
x=5