Determine if the system of equations has one solution, no solution or infinitely many solutions.

- 3x + 4y = 4

-12x + 16y = 8

x

=

0

y

=

-

2

Explanation:

simply subtract each term in the second equation from the first equation:

3

x

+

4

y

=

-

8

3

x

+

16

y

=

-

32

(

3

x

-

3

x

)

+

(

4

y

-

16

y

)

=

(

-

8

-

(

-

32

)

)

(

0

)

+

(

-

12

y

)

=

(

-

8

+

32

)

-

12

y

=

24

y

=

-

2

now use either original equation to solve for

x

:

3

x

+

4

y

=

-

8

3

x

+

4

(

-

2

)

=

-

8

3

x

-

8

=

-

8

3

x

=

0

x

=

0