Concept explainers
In Exercises 1-3, solve each system by graphing.
1.
To solve:
The given system by graphing.
Answer to Problem 1MCP
Solution:
The solution of the given system is
Explanation of Solution
Given:
Calculation:
In order to solve a pair of linear equations graphically, we follow the following steps:
Step 1:
Firstly, we re-write equation (1) as
Step 2:
We find the co-ordinates that satisfy the given equation by assigning the proper values to x.
In this way, we get three co-ordinates
Step 3:- We now plot these co-ordinates on a graph paper taking the values of x on x -axis and the values of y on y -axis and therefore we get a straight line by joining these three co-ordinates.
Step 4 :- We repeat the above steps for equation (2) and get another three co-ordinates that are (0,-4), (1,-2) and (2, 0). After plotting these points, we get another straight line.
The intersection of these two lines is a solution of the given linear equations.
Hence, the points of equation (1) are:
x | 0 | 2 | 4 |
y | 3 | 0 | -3 |
And, the points of equation (2) are:
x | 0 | 1 | 2 |
y | -4 | -2 | 0 |
Graph can be plotted as:
Conclusion:
After plotting these equations on a graph paper, we get an intersecting point i.e. (2, 0) and this is the solution of the given linear equations.
Want to see more full solutions like this?
Chapter 4 Solutions
Introductory Algebra for College Students - Learning Guide (Looseleaf)