GAUSSIAN Elimination/ Liner systems

GAUSSIAN Elimination/ Liner systems IN ORDER TO GET FULL CREDIT FOR EACH PROBLEM, \ SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY USING THE LANGUAGE OF MATH. The quiz is worth 100 points. Each problem is worth 5 points. FOR #1 AND #2, PLEASE WRITE THE AUGMENTED MATRIX FOR THE LINEAR SYSTEM. #1 x ? 3y ? 5 2x ? y ? 3 #2 6x ?12 ?5x ? 2y ? 4 FOR #3 THROUGH #8, PLEASE SOLVE THE SYSTEM BY GAUSSIAN ELIMINATION #3 0 0 0 1 0 3 ? ? ? ? ? ? #4 0 1 0 1 0 3 ? ? ? ? ? ? #5 1 0 2 1 0 1 ? ? ? ? ? ? ? #6 1 3 8 2 1 9 ? ? ?? ? ? ? ? #7 4 3 15 2 5 1 ? ? ? ? ? ? ? #8 4 2 2 2 1 1 ? ? ? ? ? ? ? ? FOR #9 AND #10, SET UP THE AUGMENTED MATRIX THAT DESCRIBES THE SITUATION, AND SOLVE FOR THE DESIRED SOLUTION. #9 One pan pizza and two beef burritos provide 1980 calories. Two pan pizzas and one beef burrito provide 2670 calories. Find the caloric content of each item. #10 A hotel has 200 rooms. Those with kitchen facilities rent for $100 per night and those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $17,000. How many of each type of room does the hotel have? FOR #11 THROUGH #15, PLEASE GRAPH THE FOLLOWING INEQUALITIES #11 x ? y ? 2 #12 x ? y ? 2 #13 3x ? 4y ?1 #14 y ?1 #15 3y ? 3 FOR #16 AND #17, GRAPH THE SYSTEM OF INEQUALITIES. SHOW (BY SHADING IN) THE FEASIBLE REGION. #16 y ?1, x ? y ? 2 #17 x ? ?1, x ?1 FOR #18 THROUGH 20, GRAPH THE SYSTEM OF INEQUALITIES. SHOW (BY SHADING IN) THE FEASIBLE REGION. IDENTIFY THE ORDERED-PAIR “CORNER POINTS” THAT DEFINE THE FEASIBLE REGION. #18 y ? ?x ? 4 , y ? ?3x ? 2 , x ? 0 , y ? 0 #19 x ? y ?1, x ? ?3y ? 2 , x ? 0 , y ? 0 #20 x ? y ?1, x ? 0 , y ? 0 BONUS (10 POINTS) Please solve 2 5 1 5 1 4 2 1 4 10 1 1 ? ? ? ? ? ? ?? ? ?? by Gaussian Elimination. 0722490842