Expert: Sherman D. - 3/26/2008

Question
Hello, my name is Sherry and I'm 52 years old and I recently returned back to school. I have solved a few of my math problems and was wondering if you can check them for me and provide the correct answers and explanations to the ones I miss and had problems solving. Please help! Thank you in advance.

18.) Solve the inequality for y. Simplify. -3y - 1 < 6/7y - 6
      y = 29/21 or 1 3/7

22.) The area of a trapezoid is given by A = 1/2h (a + b), where h is the height of the trapezoid, and a and b are the lengths of the upper and the lower base, respectively. Solve for a.
a = 2a/h - b

24.) Given an ordered pair (u, v) of numbers that satisfy the equation 6u - v = 2
     (u, v) = 2, 10

31.) Find both the x intercept and the y intercept of the line given by the equation. 2x + 7y - 13 = 0
     x intercept = -7y + 13 over 2
     y intercept = -2x + 13 over 7

32.) Find the slope of the line 3x = 4y - 3
      y = 3/4x + 3/4

34.) A line passes through the point (x,y) = (8, -8) and has a slope of -9. Write an equation for the line.
      8 + 72 = 80

36.) Write equations for the vertical and the horizontal lines passing through the point (3, 7) in (x, y)    coordinates.

vertical line is x = 3
horizontal line is y = 7

38.) Line 1: y = -2x + 3
     Line 2: y = -x + 1
     The system of equations is Consistent Independent
     This means the system has A unique solution: x=2, y=-1

     Line 1: y = -1/3x - 1
     Line 2: x + 3y = -3
     The system of equations is Consistent Dependent
     This means the system has Infinitely many solutions

     Line 1: y = 3/2x + 1
     Line 2: y + 3/2x -3
     The system of equations is Inconsistent
     This means the system has No Solution

39.) Find the value of x and y that solve the following equation.
     -8x + 3y = 7
      5x - 9y = 17
      x = -2
      y = -3

40.) Find two numbers whose sum is 47 and whose difference is 15. Call them x and y.
     x = 31
     y = 16  

Answer
18.) Solve the inequality for y. Simplify. -3y - 1 < 6/7y - 6
     y = 29/21 or 1 3/7

-3y - 1 < (6/7)y - 6
-21y - 7 < 6y - 42
-27y < -35
y < (35/27) or 1 8/27

It helps to first find the LCD and get rid of the fractions.

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22.) The area of a trapezoid is given by A = 1/2h (a + b), where h is the height of the trapezoid, and a and b are the lengths of the upper and the lower base, respectively. Solve for a.
a = 2a/h - b

A = (1/2)h(a + b), make sure to type A and a, and not have to of the same, they are completely different in algebra

2A = h(a + b)
(2A/h) = a + b
a = (2A/h) - b or a = 2(A/h) - b

so except for the A and a, you have it correct.

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24.) Given an ordered pair (u, v) of numbers that satisfy the equation 6u - v = 2
    (u, v) = 2, 10

6u - v = 2
-v = -6u + 2
v = 6u - 2

That is one ordered pair, but there are a lot others, but that will do. I don't know if they want more, or just one.

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31.) Find both the x intercept and the y intercept of the line given by the equation. 2x + 7y - 13 = 0
    x intercept = -7y + 13 over 2
    y intercept = -2x + 13 over 7

They don't want you to solve for x and y, the want the value of the point that lies on the x and y axis, this usually involves (0,y) and (x,0)

2x + 7y - 13 = 0
2(0) + 7y - 13 = 0
7y = 13
y = (13/7), so this would be (0,(13/7))

2x + 7(0) - 13 = 0
2x = 13
x = (13/2), so this would be ((13/2),0)

y-intercept is (0,(13/7))
x-intercept is ((13/2),0)

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32.) Find the slope of the line 3x = 4y - 3
     y = 3/4x + 3/4

the slope is "m" in y = mx + b

Your equation is correct, but the slope is m = (3/4)

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34.) A line passes through the point (x,y) = (8, -8) and has a slope of -9. Write an equation for the line.
     8 + 72 = 80
First of all, they want an equation, not a solution.

(8,-8), m = -9
-8 = -9(8) + b
-8 = -72 + b
b = 64

The equation is y = -9x + 64

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36.) Write equations for the vertical and the horizontal lines passing through the point (3, 7) in (x, y)    coordinates.

vertical line is x = 3
horizontal line is y = 7

Correct

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38.) Line 1: y = -2x + 3
    Line 2: y = -x + 1
    The system of equations is Consistent Independent
    This means the system has A unique solution: x=2, y=-1

Correct

    Line 1: y = -1/3x - 1
    Line 2: x + 3y = -3
    The system of equations is Consistent Dependent
    This means the system has Infinitely many solutions

y = (-1/3)x - 1
y = (-1/3)x - 1

Correct.

    Line 1: y = 3/2x + 1
    Line 2: y + 3/2x -3
    The system of equations is Inconsistent
    This means the system has No Solution

Correct

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39.) Find the value of x and y that solve the following equation.
    -8x + 3y = 7
     5x - 9y = 17
     x = -2
     y = -3

-8x + 3y = 7
5x - 9y = 17

multiply top by 3

-24x + 9y = 21
5x - 9y = 17

-19x = 38
x = -2

-8(-2) + 3y = 7
16 + 3y = 7
3y = -9
y = -3

Correct

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40.) Find two numbers whose sum is 47 and whose difference is 15. Call them x and y.
    x = 31
    y = 16

x + y = 47
x - y = 15

2x = 62
x = 31

31 + y = 47
y = 16

Correct

www.quickmath.com can show you the answer, but not how to work it, so you can check your own work for the most of it.

just make sure to change the variable, and when plotting, make sure you set the margins to what you need them. You can also do advanced, and by this i mean multiple equations to see where they all connect.