Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.

Solution Preview

The substitution method works very well when one of the equations in the system is already solved for one of the variables or can be easily solved for one of the variables. Once that equation is solved for one of the variables, the resulting expression can be easily substituted into the other equation(s) to remove that variable from the system. A simple example looks like this:

y = x + 6
x + y = 4

Notice that the first equation is already solved for y. This means that you can take the equivalent expression (x + 6) and substitute it in place of y in the second equation to get x + (x + 6) = 4. You can then solve this equation to get a value of x of -1. Then since y = x + 6, substituting -1 in for x gives a y value of 5 and the solution of the system is (-1,5).

Even though any linear equation can be solved for one ...

Solution Summary

Systems of equations can be solved in one of many different methods. A comparison is given among the substitution, elimination, and matrix methods for solving systems of linear equations.

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

Please see the attached files for the fully formatted problems.
1. Given the equation below, find f(x) where y = f(x).
8y(6x - 7) - 12x(4y + 3) + 265 - 5(3x - y + 2) = 0.
2. Solve these linearequations for x, y, and z.
3x + 5y - 2z = 20; 4x - 10y -z = -25; x + y -z = 5
3. The value of y in Question 2 lies in the ran

Hello, I am learning algebra 2. I have no help and the textbook gives very few and vague examples. Can someone help me with my algebra 2 work.
1.Find all solutions for the following system of equations. List the solutions as ordered pairs. {x^2+y^2-25 = 0
2x-y = -5
2.Solve the system of linea

1. Why do intersecting lines represent a unique solution? Give examples to support your answer.
2. What is the significance of the name 'linear equation' to its graphical representation?
3. The solutions of line m are (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471).
The solutions of line n are (3, -9)

Find the general solution ( if solution exist) of each of the following linear Diophantine equations:
(a) 2x + 3y = 4 (d) 23x + 29y = 25
(b) 17x + 19y = 23 (e) 10x - 8y = 42
(c) 15x + 51y

Please assist to understand the difference in these different methods. Please show work so I can follow the solution.
Determine if the given ordered pair is a solution to the system:
12. 2x + y = 5 (4, -3)
x - y = 1
22. 4x - y = -2 (-1, -2)
3x + y = -5
Solve each system of equations by the graphing method:

4x+y=12 (1)
x-y=8(2)
4x+y=12
x-y=8
5x/5 = 20/5
X=4
4(4) =y - 12
16+y = 12
Y =4
I think this would be an example of elimination method for solving a system of equations however I am unsure how it would transfer to substitution method thus I am needing assistance. I am needing this to be illustrated if you wi