Question

Given the system if equations

6x + 2y = -6
3x - 4y = -18

1. (0, -3)
2. (-1, 0)
3. (-2, 3)
4. (-14, -6)

Answer 1

Explanation:

Elimination-

Let's solve your system by elimination.

6

�

+

2

�

=

−

63

;

�

−

4

�

=

−

18

Multiply the second equation by -6, then add the equations together.

(6�+2�=−63)

(

�

−

4

�

=

−

18

)

Becomes:

6

�

+

2

�

=

−

63

−

6

�

+

24

�

=

108

Add these equations to eliminate x:

26

�

=

45

Then solve

26

�

=

45

for y:

26

�

=

45

26

�

26

=

45

26

(Divide both sides by 26)

�

=

45

26

Answer 2

`(- 2, 3 )`

Explanation:

`6x + 2y = - 6` → (1)

`3x - 4y = - 18` → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

`12x + 4y = - 12` → (3)

add (2) and (3( term by term to eliminate y

`15x + 0 = - 30`

`15x = - 30` ( divide both sides by 15 )

`x = - 2`

substitute
`x = - 2` into either of the 2 equations and solve for y

substituting into (1)

`6(- 2) + 2y = - 6`

`- 12 + 2y = - 6` ( add 12 to both sides )

`2y = 6` ( divide both sides by 2 )

`y = 3`

solution is
`\bold{(- 2, 3 )}`