Mark is solving the following system.
x+y+z=2 (1)
3x+2y+z=8 (2)
4x-y-7z=16 (3)
step 1: he multiplies equation (1) by 7 and adds it to equation (3).
step 2: he multiplies equation (3) by 2 and adds it to equation (2).
which statement explains mark’s mistake?
- he added equation (3) instead of equation (2) in step 1.
- he did not multiply equation (3) by the correct value.
- he did not eliminate the same variables in steps 1 and 2.
- he added equation (3) and equation (2) instead of subtracting.

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3)  4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

correct choice is C

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.

(0.2)+(-8)=0.3+-3+0.3m is the equation i guess? ?

step-by-step explanation: