Equations of Lines and Solving Systems of Linear Equations ( Simultaneous Equations )

1. Find the slope of the line that passes through the points (2, 3) and (5, 8).

2. Find the equation of the line that passes through the points (3, -2) and (4, -2).

3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 6 and passing through (-3, 5).

4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
-3x + y = 1
5x + 2y = -4

5. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
-7x + y = 8
2x - y = 2

6. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
3x - 2y = -7
-9x + 6y = 21

Solution Summary

Equations of Lines and Solving Systems of Linear Equations are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

3. (a) Solve the following systems of equations
i)
x + 2 y - z = 2
-3 x - y + z = -3
- x+ 3 y - z = 1
ii)
4 x+ -3 y+ z = - 1
-3 x+ y+ -5 z = 0
-5 x -4 z = 0
iii)
x1 + x2 + x3 = 3
-3 x1 -17 x2 + x3 + 2 x 4 = 1
4 x -7 x2 + 8 x3 -5 x4 = 1
-5 x2 -2 x3 + x4 = 1
(b) Find the values of k for which

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

1) For the equations, you are learning several methods of finding the solution to a system. Is there a difference in the result you get using an algebraic method and what you get using a graphical method? Why or why not? How does the graph of two linearequations relate to the number of solutions to the system? How could you

For solving a system of equations, is there a difference between using an algebraic method and using the graphical method? Explain why or why not, and include a numerical example to illustrate your point.

i) Solve he following equation by the quadratic formula :
3X^2 + 4X -23 = 0
ii) Find the values of x and y that satisfy the equations here given
( use the simultaneous equation method ) :
3x + 2y = 22
2x + 3y = 23
iii) Solve graphically the following equations: show the graph as a part of the solu

1. How do you interpret the solution of a system of equations by the corresponding graph?
2. Is there a basic difference between solving a system of equations by the algebraic method and the graphical method? Why?
3. Which method do you think is better for solvinglinearequations - addition or substit

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? Consider some of your responses by indicating pros and cons that you may not have considered or p

1. Determine which of the following are linearequationsand which are not linearequations. State the reason for your answer.
(a) x + y = 1000
(b) 3xy + 2y + 15z - 20 = 0
(c) 2xy + 4yz = 8
(d) 2x + 3y 4z = 6.