4 x minus Y is equal to 8 and 5 x + 5 Y is equal to 5 ,solve by cramer's rule
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Class 12
>>Applied Mathematics
>>Determinants
>>Methods of Solving System of Linear Equations
>>3x + 4y + 5z = 18 , 2x - y + 8z = 13 , 5
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3x+4y+5z=18, 2x−y+8z=13, 5x−2y+7z=20. Solve the above system of equations by Cramer's method.
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Given equations are 3x+4y+5z=18,2x−y+8z=13,5x−2y+7z=20
D=
∣
∣
∣
∣
∣
∣
∣
∣
3
2
5
4
−1
−2
5
8
7
∣
∣
∣
∣
∣
∣
∣
∣
=3(−7+16)−4(14−40)+5(−4+5)
=3(9)−4(−26)+5(1)=27+104+5=136
D
1
=
∣
∣
∣
∣
∣
∣
∣
∣
18
13
20
4
−1
−2
5
8
7
∣
∣
∣
∣
∣
∣
∣
∣
=18(−7+16)−4(91−160)+5(−26+20)
=18(9)−4(−69)+5(−6)=162+276−30=408
D
2
=
∣
∣
∣
∣
∣
∣
∣
∣
3
2
5
18
13
20
5
8
7
∣
∣
∣
∣
∣
∣
∣
∣
=3(91−160)−18(14−40)+5(40−65)
=3(−69)−18(−26)+5(−25)=−207+468−125=136
D
3
=
∣
∣
∣
∣
∣
∣
∣
∣
3
2
5
4
−1
−2
18
13
20
∣
∣
∣
∣
∣
∣
∣
∣
=3(−20+26)−4(40−65)+18(−4+5)
=3(6)−4(−25)+18(1)=18+100+18=136
Now, x=
D
D
1
=
136
408
=3
y=
D
D
2
=
136
136
=1
z=
D
D
3
=
136
136
=1