I had 50 questions and I am lost with these last ones?

Question

Please help..
48.Solve the system by substitution.
x + y = 12
y = 2x
50.Solve the following system of linear inequalities by graphing.
x – 3y > 6
3x + 2y > 12
33.A principal of $5000 was invested in a savings account for 4 years. If the interest earned for the period was $400, what was the interest rate?

Answer 1

The first one is really pretty easy, just do what they ask you to do. Substitute.
So you would replace y anywhere that it was found in the first equation with 2x (y=2x holds true for both equations if they are in a system)
That would give you
x+2x=12
Then you would need to add like terms (the x's)
Which would be
3x=12
Now you need to get the x by itself with no number in front of it (coefficient)
To do this you divide both sides of the equation by the coefficient of the x
Which gives you
x=4
Now that you know the x, you can just plug it into the equation y=2x
Which would mean
y=8
Does that help?

The second one is a little bit harder to show you how to do on yahoo answers, but ill do my best to get it to a place where you can finish it on your own.
First, you need to arrange it into the standard y=mx+b format (where m and b are real numbers and m is the slope).
You would do that by getting a positive y by itself
x-3y>6
x-x-3y>6-x
-3y>6-x
Here's where the fact that it is not an equality makes it a little tricky. When you divide both sides by -3 (to get y alone) you also have to change it from y is greater than to y is less than. With me so far?
So then you would come out with a problem like this
y<-2+1/3x
You would then graph the line like any other.
Since I can't draw you a graph I will give you a few points that would be in the line :)
(0,-2) I got this one from the fact that -2 is the y intercept
(3,-1) I just substituted a 3 for the x
Two should be enough to get you started.
Now the tricky part of the graph is that because it's < and not equal to the line has to be dotted. Also, as with any inequality that you graph, you have to shade to one side or the other of the line. Because in this equation it is <, you would shade down, or to the left of the line.
The other one is much the same :)

The last one is trickier.
The way that I learned it is to use a formula that involves the imaginary number "e". Also the question arises as to whether the intrest rate was compounded or not...I'm sorry if this isn't making any sense to you.
If it is and the intrest rate is compounded you would use the formula:
A (which is the ending ammount) = P (the beginning ammount) times "e" (an immaginonary number that if you dont know what it means just read the chapter more carefully and find out the answer for yourself) raised to the intrest rate times the time.
Which would be:
5400=5000e^4r
Divide both sides by 5000
10.8=e^4r
Take the natural log of both sides, which gets rid of the e
ln1.8=4r
Use your calculator to find ln400
.077=4r
Then divide that by 4
.019=r
and then times the number that equals r (.019) by 100 to get it in precent
So your intrest rate is:
1.9%
sorry again for the lame help on the last one :)

Answer 2

48.

x + y = 12
y = 2x

To solve this problem by substitution, in the first equation, solve one variable in terms of the other. Note that x = 12 - y.

Now, plug this into the second equation.

y = 2(12 - y)
y = 24 - 2y
3y = 24, therefore y = 8.
Plug y = 8 into the first equation, to get x + 8 = 12, x = 4.

Therefore, x = 4, y = 8.

50.

x - 3y > 6
3x + 2y > 12

Your first step would be to put it in y = mx + b form as if it were an equality rather than an inequality.

x - 3y > 6
-3y > -x + 6. Now, we're going to divide both sides by -3. This will flip the inequality sign.

y < (1/3)x - 2

At this point, what you would is graph the line y = (1/3)x - 2 as a _dotted_ line. To determine whether you shade above or below the line, test the point (0,0); that is x = 0, y = 0. If it makes the inequality true, then you shade that region; otherwise, shade the other region.

y < (1/3)x - 2
0 < 0 - 2
0 < -2, which is a false statement. So shade the portion of the line that does NOT include (0,0).

For 3x + 2y > 12, do the same thing.
2y > -3x + 12
y > (-3/2)x + 6

Create the line y = (-3/2)x + 6 as a dotted line. Now, test (0,0) again to see if you get a true or false statement.

0 > 0 + 6
0 > 6, which is a false statement. Therefore, shade the region which does NOT include (0,0) of the line y = (-3/2)x + 6.

Now that you've shaded regions on a graph, determine where the shades intersect. That will be your solution set.

Answer 3

48: x + y =12
substitute y for 2x
x+ 2x = 12
3x =12
x=4
y=2x=8
.....

50: you have to draw the two lines on a graph and shade the correct sides of the line

33: 400 over 4 years is 100 per year. 100/5000 = 2%

Answer 4

48. so becausse y=2X that means that x + y = 12 is actually x + 2x = 12 so 3x=12.... x=4

50. graph them on a calculator and then tell the place of where they intersect

33. 5400=5000e^4r
1.08=e^4r
ln1.08=4r
0.019=interest rate= 1.9 %

Answer 5

#48) X = 4
x+2x=12 (same as 1x+2x=12... 3x=12....x=3/12.... x=4)
#33) $5000x=$400.... x=$400/$5000... x=.08 or 8%

Answer 6

48.
x=4
y=8
i dont want to type anymore...