Question

If |
2 −y
1 x
| = 16 and |
3 2
y x
| = 3, then form two simultaneous equations from the given

determinants and solve.

Answer 1

Answer:

x=5, y=6

Step-by-step explanation:

in the first determinent we get

2x+y=16 is eq 1

in the second determinent we get

3x-2y=3 is eq 2

we multiple the eq 1 with 2

we get

4x+2y=32

3x-2y=3

the -2y+2y get cancel

we have 7x=35

x=5

sub x=5 in eq 1 we get 10+y=16

y=16-10=6

Answer 2

Answer:

The value of x is 5 and y is 6

Step-by-step explanation:

Given determinants are:  $\left|\begin{array}{cc}2&-y\\1&x\end{array}\right|$ and  $\left|\begin{array}{cc}3&2\\y&x\end{array}\right|$

Also, it is given that,  $\left|\begin{array}{cc}2&-y\\1&x\end{array}\right|$  = 16

Therefore, on solving, we get

2*x - (1*(-y)) = 16

=> 2x - (-y) = 16

=> 2x + y = 16                                        --(i)

Also, given that  $\left|\begin{array}{cc}3&2\\y&x\end{array}\right|$ = 3

Therefore, on solving, we get

3*x - (2*y) = 3

=> 3x - 2y = 3                                         --(ii)

Therefore, the equations are:

2x + y = 16  and 3x - 2y = 3  

Solving them simultaneously

Multiplying equation (i) by 2

=> 4x + 2y = 32

     3x - 2y =   3  

Adding them,

=> 7x = 35

=> x = 5

Substituting the value of x in equation (i)

=> 2*5 + y = 16

=> 10 + y = 16

=> y = 16 - 10

=> y = 6

Therefore, the value of x is 5 and y is 6