To find : the solution to the given system of linear equations

Expert Solution & Answer

Answer to Problem 23E

The solutions to the given system of equation are (4,1,2)

Explanation of Solution

Given information : The system of equation is {x+y+z=72x−y+z=93x−z=10

Concept Involved:

Solution of a system of equation is the point which makes both the equation TRUE.

Graphically the solution to the system of equation is the point where the two lines meet.

Method of Substitution:

1. Solve one of the equations for one variable in terms of the other.

2. Substitute the expression found in Step 1 into the other equation to obtain an equation in one variable.

3. Solve the equation obtained in Step 2.

4. Back-substitute the value obtained in Step 3 into the expression obtained in Step 1 to find the value of the other variable.

5. Check that the solution satisfies each of the original equations.

Method of Elimination:

To use the method of elimination to solve a system of two linear equations inx and y, perform the following steps.

1. Obtain coefficients for x (or y) that differ only in sign by multiplying all

terms of one or both equations by suitably chosen constants.

2. Add the equations to eliminate one variable.

3. Solve the equation obtained in Step 2.

4. Back-substitute the value obtained in Step 3 into either of the original

equations and solve for the other variable.

5. Check that the solution satisfies each of the original equations.

Calculation:

Description	Steps
Label the given equations	x+y+z=7	▶ 1^s^t equation
	2x−y+z=9	▶ 2ⁿ^d equation
	3x−z=10	▶ 3^r^d equation
In order to eliminate variable z we can add 1^s^t and 3^r^d equation	x+y+z=73x −z=10_ 4x+y =17
Label the new equation as 4^t^h equation	4x+y=17 be the 4th equation
In order to eliminate variable z we can add 2ⁿ^dand 3^r^d equation	2x−y+z=93x −z=10_ 5x−y =19
Label the new equation as 5^t^hequation	5x−y =19 be the 5th equation
In order to eliminate the variable y we need to add 4^t^h and 5^t^h equation	4x+y=175x−y=19_ 9x =36
Solve the resulting equation 9x=36 By dividing 9 on both sides of the equation Simplifying fraction on both sides	9x9=369 x=4
Substituting 4 for x in the 4^t^h equation and solve for y By subtracting 16 on both sides Combining like terms	4(4)+y=1716+y=1716+y−16=17−16y=1
Substituting 4 for x , 1 for y in 1^s^t equation	4+1+z=75+z=75+z−5=7−5z=2
Checking the solution (4,1,2) by substituting in 1st equation x+y+z=7	4+1+2=77=7 TRUE
Checking the solution (4,1,2) by substituting in 2nd equation 2x−y+z=9	2(4)−1+2=98−1+2=99=9 TRUE
Checking the solution (4,1,2) by substituting in 3rdequation 3x−z=10	3(4)−2=1012−2=1010=10 TRUE

Conclusion:

The solution to the given system of equation is (4,1,2)

Chapter 7.3, Problem 22E

Chapter 7.3, Problem 24E

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - 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