Mat 117 Problem Set 6: System Of Equations

Mat 117 Problem set 6 (System of Equations) Write your name and date

1. Solve the following systems of equations: a) 3x  y  8
15 x  2 y  26
a) solution x  c) No solution , y

Write your answer here: b) Many solutions {( x, y ) | x  , y any real number} b)

3x  y  8 15 x  5 y  13
a) solution x  c) No solution , y

Write your answer here: b) Many solutions {( x, y ) | x  , y any real number} c)

5x  y  8 15 x  3 y  24
a) solution x  c) No solution , y

Write your answer here: b) Many solutions {( x, y ) | x  , y any real number}

2. Use matrix method (Augmented form) and solve the following systems: a) x  3 y  4 z  21
2x  y  z  7 2 x  3 y  3z  19

a) solution x  c) No solution

, y…show more content…
Identify if the order triple (1,  2,3) is a solution of the given system of equations.
3x  5 y  z  16 7 x  y  3z  4 x  5 y  7 z  10

4. Identify if the system of equations given below has unique solution, infinitely many solutions, or no solution.
2 x  5 y  16 3x  7.5 y  24 5. Given is the augmented matrix of a system of equations:

1  5 6 2  7 1  3 5    1 5 7 13   Write the new form of the augmented matrix after the following row operations.
R1  r1  r3 , R2  r2  7r3

    

    

6. Four times the number of white marbles exceeded 9 times the number of red marbles by 10. The ratio of blue marbles to red marbles was 3 to 1. There is a total of 65 marbles of all 3 colors. Form a system of equations with variables red marble: r, white marble: w, and blue marble: b. Use inverse matrix method to solve the system and determine how many are white, haw many are red and how many are blue