Solve the system of linear equations 30x+50y=100 3x-15y=30

(x, y) = (5, -1)

Step-by-step explanation:

First of all, look at the equations. The first would be in standard form if it were divided by 10. (Here, we're calling this process "normalization," for lack of a better term) Doing that gives coefficients of 3, 5, 10. The second would be in standard form if divided by 3. Doing that gives coefficients 1, -5, 10.

At this point, you observe a couple of opportunities to use elimination to solve these equations. Since the x-coefficients match after the first normalization, we can subtract one equation from the other at that point. (That is what we did below.)

Since the y-coefficients are opposites after the second normalization, we could simply add the two equations to eliminate y. Either way rapidly gets you to an answer.

Choose an approach and work the problem

Divide the first equation by 10 and subtract the second equation.

... (3x +5y) -(3x -15y) = (10) -(30)

... 20y = -20

... y = -1

From either equation we can find x. Using the second one ...

... 3x -15(-1) = 30

... 3x = 15 . . . . . . subtract 15

... x = 5 . . . . . . . . divide by 3

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.