Rates and Investments : Systems of Equations Problem

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 interest would have been the same. Find the principal and the rate.

Assume that the principal and the rate are M and r, respectively. So, we have

...

Solution Summary

Rates and Investments and Systems of Equations Problem are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Problem 1. Investments. William opened two investment accounts for his grandson's college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was invested at each rate?
Problem 2.
"Arctic Antifreeze" is

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 equationsand 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) 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 andsystems with infinitely many solutions, using set notation to express their solution sets.
4) Can't type fractions, so

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

10. solve the system by graphing
y=2x+1
X+y=-2
The graphs of the following systems are given in (a) through
(d). Match each system with the correct graph.
a-d graph lines intersect at the following points
a. (-3,2)
b. (-3,-2)
c. (3,-2)
d. (2,3)
21. 5x+4y=7
x-3y=9
22. 3x-5y=-9
5x-6y=-8
23. 4x-5y=-2
3y-x=-3
24.