Download 1. Solve the following systems of equations: a) 3 8 15 2 26 x y x y +

Mat 117 Problem set 6 (System of Equations)
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1. Solve the following systems of equations:
a)
3x  y  8
15 x  2 y  26
a) solution x  , y 
Write your answer here: b) Many solutions {( x, y) | x  , y any real number}
c) No solution
b)
3x  y  8
15 x  5 y  13
a) solution x  , y 
Write your answer here: b) Many solutions {( x, y) | x  , y any real number}
c) No solution
c)
5x  y  8
15 x  3 y  24
a) solution x  , y 
Write your answer here: b) Many solutions {( x, y) | x  , y any real number}
c) No solution
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  , y  , z 
Write your answer here: b) Many solutions {( x, y, z ) | x  , y,z any real numbers}
c) No solution
b)
x  2 y  6  4z
x  13z  6  y
2 x  4 y  8 z  12
Write your answer here:
a) solution x  , y  , z 
b) Many solutions {( x, y, z ) | x 
, y=
, z is any real number}
c) No solution
3. 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 marbles.