Broadway Presents:
MARVELOUS MATH
 You
have just entered...Jill McB's web page!
Now, don't get too excited I'm a normal person just like you....can you believe it??? As you make your long, dramatic journey you will find that Mrs. Felz Algebra 2 class has been diving into substitution problems. I know what you must be thinking...well, you're scared, right? Well....this page is designed to erase all of your difficult memories dealing with this wretched word: substitution. (you can thank me later)! |
The Very First
Substitution Problem is:
|
|
STEP 1: y = 6 – 2x STEP 2:
3x
+ 4(6 – 2x) = 4
3x + 24 – 8x = 4 -5x = -20 x
= 4
STEP 4: 2x + y = 6 y = -2 The answer is: (4,-2) |
STEP 1:
STEP 2:
Y and 6 – 2x are equivalent.
We can substitue 6 – 2x for y in the second equation.
STEP 3:
This gives us an equation
in one variable, doesn’t it?? Well, now we can solve for x.
STEP 4:
Good. Now we can substitute
4 for x in either equation and solve for y.
|
| Ok. Now that you have apparently made it through the substitution problems....I graduate you to the level of linear combinations! (That's what you get for being smart!) |
|
| Step 1: We know that 3x - 4y and
-1 are equivalent expressions. Thereforee, we can use the addition property
to add the same quantity to both sides of the second equation. We then
can add 3x - 4y to the left side and -1 to the right side of the second
equation.
Step 2: Now we can solve this equation easily, finding y=1/2. Then, we substitute 1/2 for y in either of the original equations. |
Step 1: -3x + 2y + (3x
- 4y) = 0 ++ 1(-1)
Step 2: -3x
+ 2y = 0
|
linear combination problem:
|
 A
bear arrives at the Roberts' store with 8 small boxes and 5 large boxes.
The total charge for the boxes, without tax or delivery charges, is $184.
A large box costs $3 more than a small box. What is the cost of each size
box? |
| Step 1: 8x + 5y = 184
y= 3 + x Step 2: If you would like to check your answer then... 8 times $13($104) plus 5 times $16($80) is $184. $16 is $3 more than $13. Therefore, both conditions are satisfied! A large box costs $16, a small box costs $13. |
Step 1: There are two statements
in the problem. Each can be translated into an equation.
x= the cost of a small box. y= represents the cost of a large box. Step 2: When we substitute 3 = x for y in the first equation, we get 8x + 5(3 +x) = 184. When we solve for x we realize that x=13. Since y= 3 + x, y=16. |
