To explain:
The difference between the graph of a system of linear equations that has infinitely many solutions and no solution
Answer to Problem 2E
A system of linear equations that has infinitely many solutions is single line graph which shows that it has the system of two linear equations are same.
A system of linear equations that has no solution is parallel line graph which shows that it has the linear equations do not intersect.
Explanation of Solution
A system of linear equations is formed by two equations. The solution of a system of equations is an ordered pair which satisfies these two equations successfully.
The number of solutions of system of linear equations has categorized as:
- No solution
- One solution
- Infinitely many solutions
Graph of system of linear equations that has infinitely many solutions:
A graph of two linear equations or system is said to be infinitely many solutions graph when the equations are same. When the system of linear equations has exactly same equation is known as dependent system.
The system of linear equations that has infinitely many solutions is a single line graph.
Graph of system of linear equations that no solution:
When the graphs of linear equations do not intersect with each other, it is said to be that the system linear equations has no solution.
The system of linear equations with no solution is known as inconsistent system.
The graph of system of linear equations that no solution is parallel line graph which is shown by the following figure:
Chapter 5 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
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