Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.2x + 2y + 4z = 16x-2y+3z= -1x+2y-3z=-9a. (-1, 2, 22)b. (-10, 22, 42)c. (-1, 2, 4)d. (-10, 2, 22)

x = -5, y = 31/7, and z = 30/7

Step-by-step explanation:

Step 1: Convert the system into the augmented matrix form:

•224|16  

•1-23|-1

•12-3|-9

Step 2: Divide row 1 by 2 and multiply row 2 with -1 and add it into row 3:

•112|8

•1-23|-1

•04-6|-8

Step 3: Divide row 3 by 2 and multiply row 1 with -1 and add it into row 2:

•112|8

•0-3      1|-9

•02-3|-4

Step 4: Multiply row 2 with 2/3 and add it into row 3:

•112|8

•0-3      1|-9

•00-7/3|-10

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

•x + y + 2z = 8  

•-3y + z = -9

•(-7/3)z = -10 (This implies that z = 30/7.)

Step 6: Since we have calculated z = 30/7, put this value in equation 2:

•-3y + 30/7 = -9

•-3y = -93/7

•y = 31/7.

Step 7: Put z = 30/7 and y = 31/7 in equation 1:

•x + 31/7 + 2(30/7) = 8

•x = 8 - 60/7 - 31/7

•x = -5.

The mentioned options are incorrect (it can be verified by substituting all the options in the system one by one).

So final answer is x = -5, y = 31/7, and z = 30/7!!!

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!