Question

Your math teacher has a total 8 bonus points to give out to his 2 classes. Based on their effort in the review game, class 1 gets 4 less than 2 times the amount of class 2. How many bonus points does each class get? In order to graph, let class 1 be x and class 2 be y.

Answer 1

Let class 1 = x and class 2 = y

doh it already says that anyways lets dissect this sentence

Class 1 gets 4 less than 2 times the amount of class 2

now first "Class 2 is multiplied by 2" so we know we'll have 2y in this equation

Answer 2

next lets look at "class 1 gets 4 less than 2y

so lets take some values....

if 2y = 10, than the amount class 2 gets is 6 because that is 4 less than 2y

so to write this down as an equation x will always equal 2 times y minus 4

x=2y-4

Answer 3

to graph this it'd be easier to solve for y

\[x+4=2y\]
\[\frac{1}{2}x+2=y\]

Answer 4

now we have to do the first sentence also.. "your teacher can give out only 8 points to both classes, together".... this means that class 1's points and class 2 points must equal 8 or

x+y=8

Answer 5

solving this for y, you get y=-x +8

Answer 6

point intercept form is

\[y=mx+b\] which is what i did... it's much easier to graph it this way because

\[b=y intercept=(0,y)\]

Answer 7

so can you try graphing this using (0, b) as one point and using rise/run?

Answer 8

yep both are in intercept form now

\[y=\frac{1}{2}x+2\]
\[y=-x+8\]

can you graph these or is that the step you're having trouble with?

Answer 9

\[\frac{1}{2}x+2=-x+8\]
\[\frac{3}{2}x=6\]
\[x=6*\frac{2}{3}\]
\[\frac{12}{3}=4\]
\[x=4\]
using either equation

\[y=-x+8\]
\[y=-4+8\]
\[y=4\]
solution is (4,4) you're right =]

Answer 10

no problem

Answer 11

If you need any more help, let me know