Question

Solve the system by using a table. . 3y=4x+7 . -4x-4y=28. A. (-4,-3). B. (-3,-4). C.(4,3). D.(3,4)

Answer 1

For this case we have the following system of equations:

`3y = 4x + 7`

`-4x-4y = 28`

Rewriting the equations we have:

`y = ((4)/(3)) x + ((7)/(3))`

`y = -7 - x`

Then, we write a table for each function in the following interval:

[-4, 4].

We have then:

For
`y = ((4)/(3)) x + ((7)/(3))`:

-4 -3

-3 -1.666666667

-2 -0.333333333

-1 1

0 2.333333333

1 3.666666667

2 5

3 6.333333333

4 7.666666667

For
`y = -7 - x`:

-4 -3

-3 -4

-2 -5

-1 -6

0 -7

1 -8

2 -9

3 -10

4 -11

Therefore, the ordered pair solution is the one that has the same value in both tables.

We have then:

(-4 , -3)

Answer:

The solution is:

A. (-4,-3)

Answer 2

The two equations given in the question are:
3y = 4x + 7
- 4x - 4y = 28
Now, let us subtract 3y and 7 from both sides of the first equation
3y - 3y - 7 = 4x + 7 - 3y - 7
- 7 = 4x - 3y
This can be written as
4x - 3y = - 7
Now let us set the two equations in table form
4x - 3y = - 7
- 4x - 4y = 28
We get from the above deduction,
- 7y = 21
y = - 21/7
y = - 3
Now let us put the value of y in the first equation, we get
3y = 4x + 7
3 (- 3) = 4x + 7
- 9 = 4x + 7
4x = - 9 - 7
4x = - 16
x - - 4
So (x,y) comes out to be (-4, -3). The correct option among all the options given in the question is the first option or option "A".