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Chapter 4: Q 4.64 (page 425)

Solve the system by elimination: 4x+y+z=-1-2x-2y+z=22x+3y-z=1

Short Answer

Expert verified

The solution of given system of equation is (-2,3,4).

Step by step solution

01

Step 1. Given information 

We are given system of linear equations

4x+y+z=-1-(1)-2x-2y+z=2-(2)2x+3y-z=1-(3)

02

Step 2. Solving equations

Subtracting the first and second equation, we get

4x+2x+y+2y+z-z=-1-26x+3y=-3-(4)

Now, adding second and third equation, we get

-2x+2x-2y+3y+z-z=2+1y=3

Putting the value of yin fourth equation, we get

6x+3(3)=-36x+9=-36x=-12x=-2

Now, putting the value of x,yin first equation, we get

4x+y+z=-14(-2)+3+z=-1-8+3+z=-1z=-1+5z=4

Hence the solution is (-2,3,4).

03

Step 3. Checking the solution 

Checking the solution by putting the value of x,y,zin the equations, we get

4x+y+z=-14(-2)+3+4=-1-8+7=-1-1=-1-2x-2y+z=2-2(-2)-2(3)+4=24-6+4=22=22x+3y-z=12(-2)+3(3)-4=1-4+9-4=11=1

This is true, hence the solution is correct.

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Write an application problem similar to Example 4.14. Then translate to a system of equations and solve it.

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