They're all similar. Problem one you need to think how can I eliminate one of the variables to solve for the other one. Think muliplication in your head when doing this but as same time look for a way to subtract the variable you are eliminatiing should equal 0 then you solve the varialbe by itself. After you find one variables solution you need to substitute that solution into the variables place from one of the two original equations. I would think multiplying the -2y by 3 and 3y by 2. Notice one has a negative and other is positive so when I add the two equations I'll get 0y. However do not forget to multiply both equations by the multiplied number you used to each term in the equation. you should get 35x = 35 then x=1. Now you need to find y by substituting the 1 for either x-value in the two equations such as 4(1) + 3y = -5 now just solve for y and you get y = -3. your answer should be (1, -3). Notice you can always check and verify your right by substituting your values found into both solutions to get 15 = 15 and -5 = -5.
This is a very interesting problem. What makes it so interesting is that
there's so little actual math to it. The only big Math thing you need to know
in order to work with this question is the definition of "perimeter".
"Perimeter" means
"the distance all the way around the edge of something".
The problem GIVES you the length of all the sides of both triangles.
To find the perimeter of one triangle, just take the lengths of its three
sides and addum up.
The perimeter of the blue one is (7x+7) + (5x-4) + (4x+2) .
That's it ! That's the perimeter. Of course, they want you to write
it in simplest form, so you have to clean it up. Remove all of the
parentheses, add up all the 'x's, and add up all the plain numbers,
and you'll have a short, pretty expression.
Then do the same thing for the red one, and get its perimeter.
In part-b, they want you to find the difference between the two perimeters.
No problem. Just write (the blue perimeter) minus (the red perimeter),
and simplify THAT expression.
Now they want the actual perimeters when 'x' is 3.
No big deal. Just take each separate perimeter, write '3' in place of 'x',
and find the number that the expression becomes.
Just now, looking at the picture without writing anything down,
I got 53 for the blue one and 17 for the red one.
I could easily be wrong, so you definitely have to work them
out for yourself.
You determine it by finding it
Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
