Question

Find the value of unknown variables if
1. (x + y, x - y) = (3, 1)

2. (x + 2y, 3x - 2y) = (3, 1)

3. (x - 2y, 2x - 4y) = (1, 2)

4. (x + y, 4x - 2y) = (7, 10)

5. (x + y , x - 2y ) = (10, -5)

Answer 1

Answer:

Correct option is A)

Given linear equations are 3x+2y=1,2x−3y=5

Using Cramers rule, find the determinant of the coefficient

matrix,

D=

∣

∣

∣

∣

∣

∣

3

2

2

−3

∣

∣

∣

∣

∣

∣

=3×−3−(2×2) $= -9 - 4$$ =−13

Secondly, find the determinant of x coefficient matrix,

D

x

=

∣

∣

∣

∣

∣

∣

1

5

2

−3

∣

∣

∣

∣

∣

∣

=1×−3−(5×2) =−3−10=−13

Similarly, find the determinant of y coefficient matrix,

D

y

=

∣

∣

∣

∣

∣

∣

3

2

1

5

∣

∣

∣

∣

∣

∣

=3×5−(2×1) =15−2=13

Applying Cramer's rule,

x=

D

D

x

∴x=

−13

−13

=1

y=

D

D

y

∴y=

−13

13

=−1

Therefore, x=1,y=−1

Step-by-step explanation:

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