Use Cramer’s Rule to solve (if possible) the system of linear equations. 4x-y-z=1 2x+2y+3z=10 5x-2y-2z=-1

Wribreeminsl 2021-02-05 Answered
Use Cramer’s Rule to solve (if possible) the system of linear equations.
4x-y-z=1
2x+2y+3z=10
5x-2y-2z=-1
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Expert Answer

Margot Mill
Answered 2021-02-06 Author has 106 answers
Step 1
Given system of equations are
4x-y-z=1
2x+2y+3z=10
5x-2y-2z=-1
Firstly, we will find determinant of coefficient matrix.
D=[411223522]=4|2322|(1)|2352|1|2252|
D=4(-4+6)+(-4-15)-(-4-10)=8-19+14=3
Step 2
Now, we will find the following determinants.
D1=[1111023122]=1|2322|(1)|10312|1|10212|
D1=(4+6)+(20+3)(20+2)=217+18=3
D2=[4112103512]=4|10312|1|2352|1|21051|
D2=4(20+3)(415)(250)=68+19+52=3
D3=[4112210521]=4|21021|(1)|21051|+1|2252|
D3=4(2+20)+(250)+(410)=6
Now, solution of given system of equations is
x=D1D,y=D2D,z=D3D
x=1,y=1,z=2
Step 3
Result: Solution of given system of equations is
x=1, y=1, z=2
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