JU, I - 4, y = -1 = (4, -1) The solution is the ordered pair (4, -1) Check by substituting these values into the original equations. EXERCISES Use the substitution method to solve each system of linear equations. 1) x = y + 3 x + 7 = 2y 2) y = 2x 3x + y = 10 3) y = 3x 5x - 2y = 1 4) y = x + 4 3x + y = 16 5)...
2. Which ordered pair is a solution of y > 5x - 2? A. (1,5) B. (2,7) C. (3,13) D. (4,4)Is it A?
Type the ordered pair that is the solution to these equations. 2x 5y -9 3x -4y 2 Be sure to put parentheses around the ordered pair Example: (a, b)
Which table shows ordered pairs that satisfy the function y = 2x + 1? A x 0 2 1 4 6 & 2 ОВ IS 1 y 0 1 3 2 5 Ос 0 -1 0 2 1 1 D 0 2 1 0 2 2
Prove that there is a unique ordered pair (x, y) where x and y are real numbers such that y=x’ and y=2x-1. (Be sure to prove both “existence" and "uniqueness.") (25 pts)
do 4,5,6 Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
for each ordered oair, determine whether it is a solution to the system of equations. clearly state it for all 4 pairs For each ordered pair, determine whether it is a solution to the system of equations. 2x-3y=-8 y=7x+9 Is it a solution? ? (x, y) Yes No (-3, -12) O (5,6) O (-1,2) O o (2,0) o
1) Solve and write the solution set. + 2x+4 1 (2x+4)(2-3)
Solve the system by any method. WRITE ANSWER(S) AS ORDERED PAIR(S). 7) y = x2 - 3 y = -2x - 3
4. One ordered pair u (V1,U2) dominates another ordered pair u-(ui,u2) iful > ข1 and U2 > Un Given a set S of ordered pairs, an ordered pair u E S is called Pareto optimal for S if there is no vES such that v dominates u. Give an efficient algorithm that takes as input a list of n ordered pairs and outputs the subset of all Pareto-optimal pairs in S. (10 points correct reasonably fast algorithm with justification, 5...