To calculate: The solution set of system of equations,
Answer to Problem 19PPS
The system of equations has infinitely many solutions.
Explanation of Solution
Given information:
The system of equations is provided below,
Formula used:
A system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.
A system of equations is said to have infinite many solutions if all the equations are equivalent to each other and every coordinate that lies on the line or plane is a solution of the equation.
Calculation:
Consider the provided system of equations as,
Recall that a system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.
So, multiply the equation
Now add the second equation and this equation as,
Now, multiply first equation by
Add this equation and the third equation to eliminate r as,
Since, both the equations are same; it means that both the equations represent the same plane.
Recall that a system of equations is said to have infinite many solutions if all the equations are equivalent to each other and every coordinate that lies on the line or plane is a solution of the equation.
So, the given system of equations lies in the same plane and hence, has infinitely many solutions.
Thus, the system of equations has infinitely many solutions.
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