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

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.