Question

For simultaneous equations in x and y, \[{D_x} = 49,{D_y} = - 63\& D = 7\] then what is x?
A.7
B.-7
C.\[\dfrac{1}{7}\]
D.\[\dfrac{{ - 1}}{7}\]

Answer 1

Hint: Given are the values for the determinant of solution of a simultaneous equation. Thus we will use the formula of Cramer’s rule to find the value of x.
Formula used:
I.Value of x is given by \[x = \dfrac{{{D_x}}}{D}\]
II.Value of y is given by \[y = \dfrac{{{D_y}}}{D}\]
Where D is the determinant obtained from the simultaneous equations.

Complete step by step solution:
Given is the value of \[{D_x}\], \[{D_y}\] and \[D\].
We need to find the value of x. We will use the formula mentioned above.
\[x = \dfrac{{{D_x}}}{D}\]
putting the values we get,
\[x = \dfrac{{49}}{7}\]
On dividing by 7 we get,
\[x = 7\]
This is the correct answer.
Thus option A is the correct option.
So, the correct answer is “Option A”.

Note: Here note that the value we obtain by using Cramer’s rule is directly given. In Cramer’s rule we form the determinants using the coefficients of the variables of the simultaneous equations either with two variables or three variables. Number of equations is equal to the number of coefficients. Then the determinants are formed and then the value of the determinant is the value of the \[{D_x}\], \[{D_y}\] and \[D\].
But here they are already given. But in the case where they are not given we need to find them.
In the above case if value of y is to be found we will use the formula directly,
\[
  y = \dfrac{{{D_y}}}{D} \\
  y = \dfrac{{ - 63}}{7} \\
  y = - 9 \;
\]
Also note that all the options have 7 in it only either the place or the sign is changed. S don’t get confused. Answer would be only one.