```Question 27268
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:
{{{p=2q+1}}}
So using "substitution" we put 2q+1 in the other equation anywhere we see p:
{{{3p-q=-12}}}
{{{3(2q+1)-q=-12}}} Distribute:
{{{6q+3-q=-12}}}Combine q's and constants:
{{{5q=-15}}}Divide:
{{{q=-3}}}

Now that we know what q is, we find p by plugging our value for q into the first equation:
{{{p=2q+1}}}
{{{p=2(-3)+1}}} Evaluate:
{{{p=-5}}}
We can double check these values within the second equation:
{{{3p-q=-12}}}
{{{3(-5)-(-3)=12}}}
{{{-15+3=12}}}Check.

Problem 2:
{{{2x+y=12}}} & {{{3x-4y=7}}}
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):
{{{2x+y=12}}} To get the y alone, we must subtract the 2x from both sides:
{{{y=12-2x}}}

Now you can use substitution the same as the other putting "12-2x" in for y in the second equation:
{{{3x-4y=7}}}
{{{3x-4(12-2x)=7}}} 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:
{{{x=4y}}}
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:
{{{60+x+y=180}}}
Because we know x is "4y" we can substitute it as:
{{{60+4y+y=180}}}
{{{60+5y=180}}}Rearrange:
{{{5y=120}}}Divide:
{{{y=24}}}

From our first equation:
{{{x=4y}}}
{{{x=4*24}}}
{{{x=96}}}

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