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9.11.2: Practice Test

  • Page ID
    116442
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    Practice Test

    Is the following ordered pair a solution to the system of equations?

    1.

    5xy=12 x+4y=9 5xy=12 x+4y=9 with (3,3) (3,3)

    For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

    2.

    1 2 x 1 3 y=4 3 2 xy=0 1 2 x 1 3 y=4 3 2 xy=0

    3.

    1 2 x4y=4 2x+16y=2 1 2 x4y=4 2x+16y=2

    4.

    5xy=1 10x+2y=2 5xy=1 10x+2y=2

    5.

    4x6y2z= 1 10 x7y+5z= 1 4 3x+6y9z= 6 5 4x6y2z= 1 10 x7y+5z= 1 4 3x+6y9z= 6 5

    6.

    x+z=20 x+y+z=20 x+2y+z=10 x+z=20 x+y+z=20 x+2y+z=10

    7.

    5x4y3z=0 2x+y+2z=0 x6y7z=0 5x4y3z=0 2x+y+2z=0 x6y7z=0

    8.

    y= x 2 +2x3 y=x1 y= x 2 +2x3 y=x1

    9.

    y 2 + x 2 =25 y 2 2 x 2 =1 y 2 + x 2 =25 y 2 2 x 2 =1

    For the following exercises, graph the following inequalities.

    10.

    y< x 2 +9 y< x 2 +9

    11.

    x 2 + y 2 >4 y< x 2 +1 x 2 + y 2 >4 y< x 2 +1

    For the following exercises, write the partial fraction decomposition.

    12.

    8x30 x 2 +10x+25 8x30 x 2 +10x+25

    13.

    13x+2 (3x+1) 2 13x+2 (3x+1) 2

    14.

    x 4 x 3 +2x1 x ( x 2 +1) 2 x 4 x 3 +2x1 x ( x 2 +1) 2

    For the following exercises, perform the given matrix operations.

    15.

    5[ 4 9 2 3 ]+ 1 2 [ 6 12 4 8 ] 5[ 4 9 2 3 ]+ 1 2 [ 6 12 4 8 ]

    16.

    [ 1 4 7 2 9 5 12 0 4 ][ 3 4 1 3 5 10 ] [ 1 4 7 2 9 5 12 0 4 ][ 3 4 1 3 5 10 ]

    17.

    [ 1 2 1 3 1 4 1 5 ] 1 [ 1 2 1 3 1 4 1 5 ] 1

    18.

    det| 0 0 400 4,000 | det| 0 0 400 4,000 |

    19.

    det| 1 2 1 2 0 1 2 0 1 2 0 1 2 0 | det| 1 2 1 2 0 1 2 0 1 2 0 1 2 0 |

    20.

    If det(A)=−6, det(A)=−6, what would be the determinant if you switched rows 1 and 3, multiplied the second row by 12, and took the inverse?

    21.

    Rewrite the system of linear equations as an augmented matrix.

    14x2y+13z=140 2x+3y6z=1 x5y+12z=11 14x2y+13z=140 2x+3y6z=1 x5y+12z=11
    22.

    Rewrite the augmented matrix as a system of linear equations.

    [ 1 0 3 2 4 9 6 1 2 | 12 5 8 ] [ 1 0 3 2 4 9 6 1 2 | 12 5 8 ]

    For the following exercises, use Gaussian elimination to solve the systems of equations.

    23.

    x6y=4 2x12y=0 x6y=4 2x12y=0

    24.

    2x+y+z=3 x2y+3z=6 xyz=6 2x+y+z=3 x2y+3z=6 xyz=6

    For the following exercises, use the inverse of a matrix to solve the systems of equations.

    25.

    4x5y=50 x+2y=80 4x5y=50 x+2y=80

    26.

    1 100 x 3 100 y+ 1 20 z=49 3 100 x 7 100 y 1 100 z=13 9 100 x 9 100 y 9 100 z=99 1 100 x 3 100 y+ 1 20 z=49 3 100 x 7 100 y 1 100 z=13 9 100 x 9 100 y 9 100 z=99

    For the following exercises, use Cramer’s Rule to solve the systems of equations.

    27.

    200x300y=2 400x+715y=4 200x300y=2 400x+715y=4

    28.

    0.1x+0.1y0.1z=1.2 0.1x0.2y+0.4z=1.2 0.5x0.3y+0.8z=5.9 0.1x+0.1y0.1z=1.2 0.1x0.2y+0.4z=1.2 0.5x0.3y+0.8z=5.9

    For the following exercises, solve using a system of linear equations.

    29.

    A factory producing cell phones has the following cost and revenue functions: C(x)= x 2 +75x+2,688 C(x)= x 2 +75x+2,688 and R(x)= x 2 +160x. R(x)= x 2 +160x. What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.

    30.

    A small fair charges $1.50 for students, $1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of $1,050. How many of each type of ticket was sold?


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