: Solve by Cramer's rule
2x + 3y = 5, y - 32 = -2, z + 3x = 4
1 MSBTE Summer 1998, W
Answers
Answer:
Step-by-step explanation:
Given equation are
2x−y+2z=4
3x+2y+3z=16
x+3y+2z=12
Δ=
∣
∣
∣
∣
∣
∣
∣
∣
∣
2
3
1
−1
2
3
2
3
2
∣
∣
∣
∣
∣
∣
∣
∣
∣
=2(4−9)+1(6−3)+2(9−2)
=−10+3+14=7
Δ
x
=
∣
∣
∣
∣
∣
∣
∣
∣
∣
4
16
12
−1
2
3
2
3
2
∣
∣
∣
∣
∣
∣
∣
∣
∣
=4(4−9)+1(32−36)+2(48−24)
=−20−4+48=24
Δ
y
=
∣
∣
∣
∣
∣
∣
∣
∣
∣
2
3
1
4
16
12
2
3
2
∣
∣
∣
∣
∣
∣
∣
∣
∣
=2(32−36)−4(6−3)+2(36−16)
=−8−12+40=20
Δ
z
=
∣
∣
∣
∣
∣
∣
∣
∣
∣
2
3
1
−1
2
3
4
16
12
∣
∣
∣
∣
∣
∣
∣
∣
∣
=2(24−36)+1(36−16)+4(9−2)
=−48+20+28=0
∴x=
Δ
Δ
x
,y=
Δ
Δ
y
,z=
Δ
Δ
z
⟹x=
7
24
,y=
7
20
,z=0
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