Question

solve the following system of linear equations by crammers rulex+2y=5,4x-3y=4

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given equations

x+2y+4z=16

4x+3y−2z=5

3x−5y+z=4

Here , Δ=

∣

∣

∣

∣

∣

∣

∣

∣

1

4

3

1

3

−5

4

−2

1

∣

∣

∣

∣

∣

∣

∣

∣

=−(3−10)−2(4+6)+4(−20−9)

=−7−20116=−143

Δ

1

=

∣

∣

∣

∣

∣

∣

∣

∣

16

5

4

2

3

−5

4

−2

1

∣

∣

∣

∣

∣

∣

∣

∣

=16(3−10)+2(5+8)+4(−25−12)

=−112−26−148=−186

Δ

2

=

∣

∣

∣

∣

∣

∣

∣

∣

1

4

3

16

5

4

4

−2

1

∣

∣

∣

∣

∣

∣

∣

∣

=1(5+8)−16(4+6)+4(16−15)

=13−160+4=−143

and Δ

3

=

∣

∣

∣

∣

∣

∣

∣

∣

1

4

3

2

3

−5

16

5

4

∣

∣

∣

∣

∣

∣

∣

∣

=1(12+25)−2(16−15)+15(−20−9)

=37−2−464=−429

Using Cramer's rule,

x=

Δ

Δ

1

=

−143

−286

=2

y=

Δ

Δ

2

=

−143

−143

=1

z=

Δ

Δ

3

=

−143

−429

=3

Hence, x=2,y=1,z=3