Determine whether the system is consistent without row reduction. If the system is consistent, provide at least one solution. If the system is inconsistent, state the reason. x1 + x2 + x3 + x4 + x5 + x6 = 10 -X1 + 2x2 -2x3 + x4 -2x5 + x6 = 200 1x1 + 3x2 + x3 + 0x4 + 3x5 + 2x6 = 100 1x1 + 0x2 + x3 + 2x4+x5 + 3x6 = 200 -x1 + x2 + 0x3 + 3x4 + 2x5 + 1x6 = 100 2x1 + 8x2 + 2x3 + 8x4 + 6x5 + 9x6 = 0

Step-by-step explanation:

X = cost of PB  

Y = cost of J

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Dividing everything in the first equation by 2:

3X + 2Y =  966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

   9X +   6Y =   2898

-10X + -6Y  = -3134

-X = -236

X =  236 --> so the price of the PB is 236 pennies or $2.36

Plugging into the second equation as the numbers are a bit smaller,

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

Now we check:  4 x $1.29 + 6*2.36 = $19.32

                       3 x $1.29 + 5 x 2.36 = $15.37

The answers are verified and highlighted in bold.

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies