SOLUTION: i am stuck on 3 different problems on my math homework(there is a test this wednesday) and like i have said before...my teacher does not care to help me nor any other students in t

Question 27268: i am stuck on 3 different problems on my math homework(there is a test this wednesday) and like i have said before...my teacher does not care to help me nor any other students in the class to understand the work he provides. so i am once again stuck!
Solve each system of equations:
1) p=2q+1
3p-q=-12
rewrite one of the equations in each system to get one of the variables alone on one side of the equation. then solve the system of equations:
2x+y=12
3x-4y=7
this one has no directions...we just have to solve it:
one angle of a triangle is 4 times as large as another angle of the same triangle. the third angle of the triangle has a measure of 60 degrees. what are the measures of the other 2 angles of the triangle?
please help me.
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
For future reference, if you have 3 questions to ask you should ask them in 3 different postings, it makes it more likely that someone will get to them. That said, let's see what I can do:
The first question you should use substitution. How do you know? Because p is by itself on one side of the equals sign, so it doesn't take any rearranging to substitute for p. We are told explicitly that:

So using "substitution" we put 2q+1 in the other equation anywhere we see p:

Distribute:
Combine q's and constants:
Divide:

Now that we know what q is, we find p by plugging our value for q into the first equation:

Evaluate:

We can double check these values within the second equation:

Check.
Problem 2:
&
He's essentially asking you to use substitution again. Only this time, it's not written straight out, we need to do a bit of rearranging to get a variable by itself. If we don't want to work with fractions, the easiest variable to get by itself is the y in the first equation (notice how it's by itself and not being multiplied by anything):
To get the y alone, we must subtract the 2x from both sides:

Now you can use substitution the same as the other putting "12-2x" in for y in the second equation:

And procede the same way as the first problem.
Problem 3: one angle of a triangle is 4 times as large as another angle of the same triangle. the third angle of the triangle has a measure of 60 degrees. what are the measures of the other 2 angles of the triangle?
This requires you to convert from english to algebra before solving the equation. And to know a little bit of geometry rules as well. First, we're talking about 3 angles of a triangle. One of them is 60. The other two we don't know, so we'll call one x and the other y.
We're told that "one angle (now called x) is (equals) 4 times as large as another (called y)..."
In other words, angle X is 4 times angle y, or:

Great, so now we know we can use substitution for x with our final equation... but what is it. You need to know to solve this problem that all angles of a triangle add up to 180 degrees. So our first angle (60 degrees) + our second (x) + our third (y) = 180 or:

Because we know x is "4y" we can substitute it as:

Rearrange:
Divide:

From our first equation:

Therefore the three angles of the triangle are 60, 24, and 96. Good luck with the test.
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