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), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240).
a. Form the equations of both the lines. Show your work.
b. What are the co-ordinates of the point of intersection of lines m and n?
c. Write the co-ordinates of the intersections of lines m and n with the x-axis.
d. Write the co-ordinates of the intersection of lines m and n with the y-axis.
Solution Summary
This discusses the graphs of equations and the solutions of systems of 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
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
Please help with the following problems. Provide step by step calculations.
Find the slope of each line that has a slope
x=5y
Find an equation in the form y=ms +b (where possible) for each line.
Through (3,-5) parallel to y= 4
Graph each linear equation defined as follows;
3x - 5y =15
Solve each system of equat
A) Find the inverse of: |2 1 1|
|0 1 2|
|2 2 1|
b) Use it to solve the following system of equations:
2x1 + x2 + x3 = 4
x2 + 2x3 = 0
2x1 + 2x2 + x3 = 1.
Please help with the following problems.
There are three methods to solving LinearSystems with two Equations. They are the Graph method, the Elimination method, and the Substitution method. When would you use each method? What makes each method better than the other methods?
Solve the following linear system using Gaussian elimination.
Show work.
2y + z = 4
x+ y +z = 6
2x + y + z = 7
Solve the following linear system for x using Cramer's rule.
Show work.
4x - y + z = -5
2x + 2y + 3z = 10
5x - 2y + 6z = 1
