Statistics 2: Solving Systems of Equations by Graphs and Substitution

This document presents a comprehensive solution to a mathematics assignment focused on solving systems of equations. The assignment is divided into two main sections: solving systems of equations by graphing and by the substitution method. Each section provides detailed, step-by-step solutions to multiple problems. The graphing section demonstrates how to find the point of intersection of two lines, representing the solution to the system. The substitution method section illustrates how to solve for variables by substituting the value of one variable from one equation into another. The solutions cover various scenarios, including systems with unique solutions, no solutions (parallel lines), and provide insights into the application of these methods. The solutions are well-organized, and easy to follow, making it a valuable resource for students studying mathematics.

Running head: MATHEMATICS
Mathematics
Name of the Student:
Name of the University:
Author’s Note:

1STATISTICS
Table of Contents
Solving Systems of Equations by Graphs:.................................................................................2
Answer 1................................................................................................................................2
Answer 2................................................................................................................................3
Answer 3................................................................................................................................5
Answer 4................................................................................................................................7
Answer 5................................................................................................................................8
Answer 6..............................................................................................................................10
Answer 7..............................................................................................................................11
Answer 8..............................................................................................................................13
Solving Systems of Equations by Substitution Method:..........................................................14
Answer 1..............................................................................................................................14
Answer 2..............................................................................................................................15
Answer 3..............................................................................................................................15
Answer 4..............................................................................................................................16
Answer 5..............................................................................................................................16
Answer 6..............................................................................................................................17
Answer 7..............................................................................................................................18
Answer 8..............................................................................................................................18

2STATISTICS
Solving Systems of Equations by Graphs:
Answer 1.
y = - (5/3)x +3 y = (1/3)x – 3
x y x y
- 6 13 - 6 - 5
- 3 8 - 3 - 4
0 3 0 - 3

3STATISTICS
The solution of system of equations is the point of intersection of the two lines, which is (x,
y) = (3, -2).
Answer 2.

4STATISTICS
y = 4x +3 y = (-1)x – 2
x y x y
- 7 -25 - 5 3
- 1 - 1 0 - 2
4 19 4 - 6
The solution of system of equations is the point of intersection of the two lines, which is (x,
y) = (-1, -1).

5STATISTICS
Answer 3.
y = - (1/2)x – 2 y = (1/4)x – 4
x y x y
- 6 1 - 8 - 6
1 - 2.5 0 - 4
8 - 6 8 - 2

6STATISTICS
The solution of system of equations is the point of intersection of the two lines, which is (x,
y) = ( 8
3 ,−10
3 ).

7STATISTICS
Answer 4.
y = - 1 y = (- 5/2)x + 4
x y x y
- 6 - 1 - 8 - 6
1 - 1 0 - 4
8 - 1 8 - 2

8STATISTICS
The solution of system of equations is the point of intersection of the two lines, which is (x,
y) = (2, -1).
Answer 5.

9STATISTICS
y = 3x – 4 y = (- 1/2)x + 3
x y x y
- 6 - 22 - 4 5
0 - 4 0 3
7 17 4 1
The solution of system of equations is the point of intersection of the two lines, which is (x,
y) = (2, 2).

10STATISTICS
Answer 6.
y = - 2x + 2 y = -2x – 2
x y x y
- 6 14 - 5 8
0 2 0 - 2
3 - 4 4 - 10

11STATISTICS
The system of equations has no solutions as both the lines of equation are parallel to each
other. No intercept could be found of these two equation lines.
Answer 7.