Question

solve determinant eqution 2x-3y=2;x-y÷2=1÷2​

Answer 1

Answer:

Correct option is

C

x=5,y=4

Given equations are 2x−3y=−2,4x−24=−y

Using Cramer's rule, find the determinant of the coefficient matrix,

D=

∣

∣

∣

∣

∣

∣

2

4

−3

1

∣

∣

∣

∣

∣

∣

=2×1−(4×−3) =2+12 =14

Secondly, find the determinant of x coefficient matrix,

D

x

=

∣

∣

∣

∣

∣

∣

−2

24

−3

1

∣

∣

∣

∣

∣

∣

=−2×1−(24×−3) =−2+72=70

Similarly, find the determinant of y coefficient matrix,

D

y

=

∣

∣

∣

∣

∣

∣

2

4

−2

24

∣

∣

∣

∣

∣

∣

=2×24−(4×−2) =48+8=56

Applying Cramer's rule,

x=

D

D

x

∴x=

14

70

=5

y=

D

D

y

∴y=

14

56

=4

Therefore, x=5,y=4

Answer 2

$2x - 3y = 2$

$x - \frac{y}{2} = \frac{1}{2}$

from equation (2)

• $x = \frac{1}{2} + \frac{y}{2}$

putting value of X in equation (1),

• $2( \frac{1}{2} + \frac{y}{2} ) - 3y = 2$
• $1 + y - 3y = 2$
• $- 3y + y = 2 - 1$
• $- 2y = 1$
• $y = \frac{ - 1}{2}$

putting value of y in equation of X,

• $x = \frac{1}{2} + \frac{y}{2}$
• $x = \frac{1}{2} - \frac{1}{4}$
• $x = \frac{2 - 1}{4}$
• $x = \frac{1}{4}$

thus the value of X = 1/4 and Y = -1/2