Question

Please Answer 1-3 for me

1. Solve the system of linear equations using the Gauss-Jordan elimination method.

2x1	−	x2	+	3x3	=	−16
x1	−	2x2	+	x3	=	−5
x1	−	5x2	+	2x3	=	−11

(x₁, x₂, x₃) = ( )

2. Formulate a system of equations for the situation below and solve.

For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $90 apiece, rear orchestra seats cost $70 apiece, and front balcony seats cost $50 apiece. The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400. The total receipts for the performance were $70,800. Determine how many tickets of each type were sold.

front orchestra
rear orchestra
front balcony

  

3.

Formulate a system of equations for the situation below and solve.

Joan and Rick spent 3 weeks (21 nights) touring four cities on the East Coast—Boston, New York, Philadelphia, and Washington. They paid $220, $440, $180, and $200 per day for lodging in each city, respectively, and their total hotel bill came to $6,360. The number of days they spent in New York was the same as the total number of days they spent in Boston and Washington, and the couple spent 3 times as many days in New York as they did in Philadelphia. How many days did Joan and Rick stay in each city?

Boston	days
New York	days
Philadelphia	days
Washington	days

Answer 1

Lt the mumber of doye they Spent in each follous city ale as Boton -b day's days P days day's New Yok Phila delphia Washington gifen the rumber of daye tay Spert Newyore doys they Spent n Was Same as the total number Beston and Wachingon times thay did ia 3 many doys in Nawyeotk as as Phi ladel phia nI3P Gaste el Stoy her day $180, and Cdy $220, $440, Cach ale $ 200 hence the total Gat 440 m+ 180 p+ 200w 2 20 b 1 equal to $6,360 giren it is 2 20b+ 440n+ 180 p+ 20ow 6360 Tetal number et days 21 b+ m+ p+w=21 4

fon and 4 2n+p=21 2 (3p)+= 21 7 P21 p 3 Herele'e b+ w=9 220 b+ 440 (9) +180(3)+ 200w = 6360 220b+ 20o w 1860 11b+1ow93 lob+10w=90 b= 3 and days 9 days 3 days Boston 3 Newyoh philadelphia Wochington

Updated