Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0? Why?

Answer 1

To check if (−2, 6) is a solution to the system of linear equations x+2y=10 and 3x+y=0, we can substitute x=-2 and y=6 into both equations and see if the left-hand side equals the right-hand side:

x+2y = 10
-2 + 2(6) = 10
10 = 10

This is true, so (−2, 6) is a solution to the first equation.

3x+y = 0
3(-2) + 6 = 0
0 = 0

This is also true, so (−2, 6) is a solution to the second equation.

Since (−2, 6) is a solution to both equations, it is a solution to the system of linear equations.

Answer 2

A company that makes basketballs has calculated their revenue and costs as follows for the most recent fiscal period:

Sales $623 000
Costs:
Fixed Costs $???????
Variable Costs 404 880
Total Costs ???????
Net Income (Loss) $(26 880)

Answer 3

To find the missing values for fixed costs and total costs, we can use the formula:

Total Costs = Fixed Costs + Variable Costs

We know that the variable costs are $404,880 and the net income is a loss of $26,880. We can use the net income to find the total costs:

Net Income = Total Revenue - Total Costs
-26,880 = 623,000 - Total Costs
Total Costs = 623,000 + 26,880
Total Costs = $649,880

Now we can use the formula to find the fixed costs:

Total Costs = Fixed Costs + Variable Costs
649,880 = Fixed Costs + 404,880
Fixed Costs = 649,880 - 404,880
Fixed Costs = $245,000

Therefore, the missing values are:

Fixed Costs: $245,000

Total Costs: $649,880