math help please?

Question

1. Use any method for solving the following system of equations:
x - 3y = 12
2x + 5y = -20

A. (6,-2)
B. (-5,-2)
C. (0,-4)
D. (12,0)

2. Mike paid $54 for his greens fee and three sleeves of balls. Matt paid $42 for his greens fee and one sleeve of balls. How much did a sleeve of golf balls cost?

A. $12
B. $6
C. $8
D. Not enough information given

3. Change this standard form equation into a slope intercept form:

3x - 4y = 24

A. y = ¾x + 24
B. y = ¾x - 6
C. 4y = -3x + 24
D. y = -3x + 8

4. (3,4) is a solution to this equation:
4x + 3y = 12

A. True
B. False

SOLVE

5. y = -1x + 4
6. y = 3x - 4
7. y = ½x + 5

8. Choose the TWO equations that represent parallel lines.

A. y = ½x + 4
B. y = ½x - 6
C. y = 2x + 4
D. y = -½x + 8

Answer 1

1) x - 3y = 12
2x + 5y = -20

2x - 6y = 24
--------------------
11y = -44
y = -4
x = 0

The answer is C. (0,-4)

2) Two sleeves of balls cost $12 (difference between the two prices). One sleeve costs $6. The answer is B.

3) B. y = ¾x - 6

4) B. False -- 4(3) + 3(4) = 12 + 12 = 24... not 12

5) What?
6) What?
7) What?

8) A. and B. (slope for both is ½)

Answer 2

1. x - 3y = 12 or 2x - 6y = 24 (multiply each side by 2)
2x + 5y = -20

then subtract the equations: (2x - 6y) - (2x + 5y) = 24 - (-20) = 44
so -11y = 44 and y=-4
x - 3y = 12 becomes x + 12 = 12 and x=0
So C is the answer

2. GF = greens fees , B = sleeve of balls
Mike: GF +3B = 54
Matt: GF + B = 42
Subtract these two and get 2B = 12 or B=6
So the answer is A

3. Standard form is y = mx + b
3x - 4y = 24 .... rearrange so 3x - 24 = 4y
Now divide both sides by 4 to get y: (3/4)x - 6 = y
so B is the answer

4.(3,4) is a solution to this equation: 4x + 3y = 12
Just substitute the values into the equation
4*3 + 3*4 =12 gives 24 = 12 and this is not true so (3,4) is not a solution
The answer is B

Solve. These are just single equations, you need two equations to solve for two variables. But if you mean you just want some point that satisfies the equations then this I can do but there are an infinite number of such solutions.
5. y = -1x + 4 ........ x=2 and y=2
6. y = 3x - 4 ........ x=2 and y=2
7. y = ½x + 5 ........ x=2 and y=6

8. parallel lines should have the same slope
A = Mx + B where M is the slope. So the slopes are
A... 1/2
B... 1/2
C... 2
D... -1/2
So A and B are the parallel lines

Answer 3

1. Multiply the top equation through by -2, then you can add the equations down to cancel out the x-terms. This leaves that 11y = -44. When you solve for y, you find that y= -4 which is answer C.
2. The two men paid the same for greens fees, so that really is just distracting information. The problem is asking how much for one sleeve of balls. The first man got one sleeve, and the second man got 3 sleeves so the difference in money paid reflects the price of 2 sleeves. Therefore the basic equation would be 2 sleeves = 12 dollars (the difference of 54-42). So one sleeve costs 6 dollars, or choice B
3.To put the equation of the line from standard form, you must manipulate the terms to be in the style of y=mx+b. This is the slope intercept form. So, subtrace 3x from both sides. Then divide both sides by -4. This gives y=3/4x -6 or B
4. False, because when you plug those points in you get 24=12. This is not a true statement so the question is not true.
Questions 5, 6, 7 dont make sense. Solve for what? They are just three line equations. Are you supposed to solve for the intersection or what. You need better directions.
8. The definition of two parallel lines is that they have the same slope. Since the question is already in slope-intercept form the only two with identical slopes are choices A and B.

Hope this helps you out, good luck in math.

Answer 4

1. Sub your x's and y's in.

2. There is $12 difference between their totals. Knowing that Mike has two more sleeves of balls than Matt, divide $12 by 2 and you get $6. One sleeve = $6

3. Slope intercept form is y =mx + b
3x - 4y = 24
-4y = -3x + 24 Subtract 3x from both sides
y = 3/4x - 6 Divide by -4 to get y by itself

4. Sub in your x's and y's
4(3) + 3(4) = 12
12 + 12 = 12
24 = 12 FALSE

5. y = -1x + 4
y - 4 = -1x Subtract 4 from both sides to isolate x
(y - 4)/-1 = (-1x)/-1 Divide both sides by -1 to get x alone
-y +4 = x

6. Follow #5
7. Follow #5

8. y = mx + b, where m is the slope; parallel lines have the same slope. Considering that A & B are the only two equations that have the same slope (m = 1/2), the answer would be A & B.

Answer 5

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