The solution set of the system of linear equations
Answer to Problem 1RE
The solution set of linear equations
Explanation of Solution
Given:
The system of linear equations is
Procedure used:
“Solving system of linear equations by elimination:
(1) If the equations are not in the standard form, then they are converted accordingly into a standard form.
(2) The variable to be eliminated is recognized from the given equations in the system.
(3) After obtaining the LCM (lowest common multiple) of coefficients of the variable to be eliminated, the equations are multiplied with appropriate multipliers so that the coefficients in each equation become additive inverses and adding the new equations will result in a fresh equation with the decided variable to been eliminated.
(4) The equation in step (3) is solved obtaining value of remaining variable.
(5) The value of variable in step (4) is substituted to the equation in any of the given system equations.
(6) Solving the equation obtained in step (5) gives the value of variable eliminated in step (3).
(7) The correctness of solution is asserted by substituting back the values in given equations of the system.
Calculation:
The given equations are, as follows:
Step 1:
Since the given equations are already in standard form, nothing has to be done.
Step 2:
The coefficient of y in equation (1) is
Step 3:
Multiply equation (1) with number
Now, add resultant equation of equation (1) and equation (2) of given system of linear equations:
The above addition gives the equation
Step 4:
Solve the equation obtained in step 3 to obtain the value of
Thus, the value of x is
Step-5:
Now, substitute
Step-6:
The equation obtained in Step (5) is solved:
Thus, the value of y is
Step-7:
In order to check whether the solution is correct or not, substitute
Substitute
Therefore, the point
Substitute
Therefore, the point
Hence, it is asserted that the value of x is
Thus, the solution set for the system of linear equations
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