Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method?

Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different?
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2. Translate. The first row of the table and the fourth sentence of the problem tell us that a total of 63 pupae was received. Thus we have one equation:
p + q = 63

Since each pupa of morpho granadensis costs $4.15 and p pupae were received, 4.15p is the cost for the morpho granadensis species. Similarly, 1.50q is the cost of the battus polydamus species. From the third row of the table and the information in the statement of the problem, we get a second equation

4.15p+ 1.50q = 147.50

We can multiply by 100 on both sides of this equation in order to clear the decimals. This gives us the following system of equations as a translation:
p + q = 63, (1)

415p + 150q= 14,750 (2)

3. Solve. We decide to use the elimination method to solve the system. We eliminate q by multiplying equation (1) by -150 and adding it to equation (2):

-150p- 150q= -9450 multiply equation (1) by -150
415p + 150q = 14,750
25p =5300 adding
P =20 solving for p

We obtain (20,43) or p=20, q=43

4. Check. We check in the original problem. Remember that p is the number of pupae of morpho granadensis and q is the number of pupae of battus polydamus.

Number of pupae p+q =20 + 43=63

Cost of morpho granadensis $4.15p + 4.15(20) = $83.00
Cost of battus polydamus $1.50q + 1.50(43)= $64.50
Total= $147.50

Solve for x and y in the following two sets of simultaneous equations:
4x-2y = 1 ......(i)
8x-4y = 1 ......(ii)
y = 2x + 3.......(i)
2y - 4x = 6 .....(ii)

Please help me solve the following system of three equations and discribe the methods that are being used to help me understand:
X + Y + Z = 6
2X - Y + 3Z = 8
3X - 2Y - Z = -17
Thank you!

1. What systems of equations can be solved by graphing or using substitution or elimination? Which method do you like best and why would it be different method. How would you answer this question?
2.Why graphing gives more visual of the problem and the elimination makes it easier to come up with the answer?

1) Solve by the addition method.
3x + 2y = 14
3x - 2y = 10
2) Solve by the addition method
5x = 6y + 50
2y = 8 - 3x
3) Solve. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
4) Can't type fractions, so

I would like to know if I am on the right track to writin this as a "systems of equations" using the substitution process. How much further do I have to go if this is right so far?
A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the in

Solve the following systems by substitution. Determine whether the equations are independent, dependent or inconsistent
36. y = -3x + 19
y = 2x - 1
38. 4 = -4x - 7
y = 3x
42. y = x + 4
3y - 5x = 6
56. 2x - y = 4
2y = 4x - 6
70. x + 3y = 2
-x + y = 1
Section 7.2
Solve each system by addition.
8. x + y

There are many applications used in the area of solving systems of equations. For example, systems of equations can be used to find the optimal number of items to produce to ensure the highest profit of those particular items. Systems of equations can be solved by four methods: graphing, substitution, elimination or with matrice