solve each of the following systems by the addition method?

Question

6x + 3y = - 1
9x + 5y = 1

Answer 1

(6x + 3y = - 1)* -5
(9x + 5y = 1)*3

-30x-15y = 5
27x+15y=3
----------------
-3x=8
x = -8/3
6(-8/3)+3y = -1
-16 + 3y = -1
3y = 15
y = 5

Answer 2

6x + 3y = - 1- - - - -Equation 1
9x + 5y = 1- - - - - -Equation 2
- - - - - - - - - -
Multiply equation1 by 5 and equation 2 by - 3

6x + 3y = - 1

5(6x) + 5(3y) = - 5(1)

30x + 15y = - 5
- - - - - - --

9x + 5y = 1

-3(9x) +( - 3)(5y) = -3(1)

- 27x + (- 15) = - 3

- 27x - 15y = - 3

- - - - - - --

30x + 15y = - 5
- 27x - 15y = - 3
- - - - - - - - - - -
3x = - 8

3x/3 = - 8/3

x = - 8/3

The answer is x = - 8/3

Insert the x value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

9x + 5y = 1

9(- 8/3) + 5y = 1

- 72/3 + 5y = 1

- 24 + 5y - 1

- 24 + 5y + 24 = 1 + 24

5y = 25

5y/5 = 25/5

y = 5

The answer is y = 5

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

Check for equation 2

9x + 5y = 1

9(- 8/3) + 5(5) = 1

- 72/3 + 25 = 1

- 24 + 25 = 1

1 = 1

- - - - - -

Check for equation 1

6x + 3y = - 1

6(-8/3) + 3(5) = - 1

- 48/3 + 15 = - 1

- 16 + 15 = - 1

- 1 = - 1

- - - - - - - - -

The solution set { - 8/3, 5 }

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

Answer 3

6x + 3y = - 1...eq.1
9x + 5y = 1...eq.2


multiply eq. 1 by -3
and multiply eq. 2 by 2

-18x - 9y = 3...eq.4
18x + 10y = 2...eq.5 now add them up
------------------
0 + y = 5

y = 5...put this value in eq.1

6x + 3y = - 1
6x + 3(5) = - 1
6x + 15 = - 1
6x = -15- 1
x = -16 / 6

x = -2.666

Answer 4

3*equation 1 gives
18x+9y=-3
2*equation 2 gives
18x+10y=2

eq.2 minus eq.1 is
(18-18)x+(10-9)y=2-(-3)
y=5

6x+3*5=-1
x= -8/3