Question

1. Solve the system by using a table. 3y=4x+7 , -4x-4y=28. These are the possible solutions: A) (–4, –3), B) (–3, –4), C) (4, 3), D) (3, 4).

2.Solve by graphing. -3x-y=-10, 4x-4y=8. possible solutions: A) (-1,3), B) (3-1), C) (1,3), D) (3,1)
3. The spreadsheet shows the monthly revenue and expenses for a new business.Use the models to predict the month in which revenue will equal expenses. Possible answers:
A) October
B) September
C) August
D) May

Answer 1

1) (A) (-4,-3)

2) (D) (3,1)

3) (B) September

Explanation:

1) 4x+7=3y

-4x-4y=28

By elimination method, we get y= -3 and x= -4

Hence (A)(-4,-3) is correct.

2) We will pot the points for the equations -3-y= -10 and 4x-4y = 8

The point of intersection is the solution that is (D) (3,1).

3) We can solve it by assuming revenue - expenses, and for revenue= expenses

We need to prove difference = 0

Let x denotes the month and y denotes the difference between revenue and expenses.

Then for January = (1,18000)

Feb = (2,15000)

march = (3,12000)

April = (4,11000)

may = (5,9000) and so on

The best fit line for the points is y= -2200x+19,600

We need y= 0

Then, x = 19,600/2200

= 8.9 = 9 (approx)

In 9th month (September) the difference will be 0 and revenue = expenses.

(B) is correct.

Answer 2

The first question:
3y=4x+7 (1)
-4x-4y=28 (2)

Let's plug in x = -4, -3, 3, and 4 and see the y-values :)

I have attached the table since it's hard to make a table with text :P
As you can see, when x = -4, that is when the y-values are equal. That means that is the solution to the system of equations. Your answer is A) (-4, -3).

The second question:
-3x-y=-10 (1)
4x-4y=8 (2)

When you graph both equations, you will see that they intersect at D) (3, 1).

The third question:
We need to find the lines for revenues and expenses.
To find the line for revenues, make months the x-value and revenues the y-values. And find the equation. You should get y = 4,100x + 300.
To find the line for expenses, make months the x-value and expenses the y-values. And find the equation. You should get y = 1,900x + 19,990.

Now graph both solutions and see where they intersect. They intersect at approximately (8.95, 36995)

That would be during the month of C) August.