Solve the following system. x2 + y 2= 25 2x + y = 10 the solution set {( a0, a1), ( a2, a3)}.

The solution set is { (3, 4), (5 , 0) }.

Step-by-step explanation:

x^2 + y^2= 25

2x   +   y =  10

We use substitution:

From the second equation y = 10 - 2x.

Substituting for y in the first equation:

x^2 + (10 -2x)^2 = 25

x^2 + 100 - 40x + 4x^2 - 25 = 0

5x^2 - 40x  + 75 = 0

Divide through by 5:

x^2 - 8x + 15 = 0

(x - 3)(x - 5) = 0

x = 3, 5.

when x = 3 , y = 10 - 2(3) = 4.

when x = 5, y = 10 - 2(5) = 0.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

the answer is d

step-by-step explanation: