In Exercises 1–12, solve each system by the method of your choice.
1.
To solve: The system
Answer to Problem 1MC
The solution set is
Explanation of Solution
Method used:
Solving Linear Systems by Substitution:
1. Solve either of the equations for one variable in terms of the other. (If one of the equations is already in this form, you can skip this step).
2. Substitute the expression found in step 1into the other equation. This will result in an equation in one variable.
3. Solve the equation containing one variable.
4. Back-substitute the value found in step 3 into one of the original equations. Simplify and find the value of the reaming variable.
5. Check the proposed solution in both of the system`s given equations.
Calculation:
The solution of the system
Step 1: Solve either of the equations for one variable in terms of the other:
In above system observed that the equation
Step 2: Substitute the expression found in step 1 into the other equation:
Substitute
From the above equation it is observed that the variable
Step 3: Solve the resulting equation containing one variable:
Solve the equation
Step 4: Back-substitute the obtained value into the one of the original equations:
Substitute 2 for
Substitute 2 for
Similarly, substitute 2 for
Here, it is cleared that the obtained values of
Thus, with
5. Check:
Check whether the proposed solution
Substitute
Similarly, substitute
Therefore, the solution set is
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Chapter 5 Solutions
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