Question

For a simultaneous equation \[x\] and \[y\] . If \[Dx = 25,Dy = 50\] and \[D = 5\] , what is the value of \[x\] ?
A. \[ - 5\]
B. \[\dfrac{1}{5}\]
C. \[10\]
D. \[5\]

Answer 1

Hint: In this give problem, we needs solve the given equation and find the value of \[x\] and \[y\] Simultaneous equations require algebraic skills to find the values of letters within two or more equations. They are called simultaneous equations because the equations are solved at the same time. If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution.

Complete step by step solution:
In the given problem,
 \[
  Dx = 25 \to (1) \\
  Dy = 50 \to (2) \\
  D = 5. \;
 \]
By this simultaneous equation in \[x\] and \[y\] , we can find the value of \[x\] and \[y\] .
To find the value of \[x\] and \[y\] from the two equation, we get
By substituting the value \['D'\] into the equation \[(1)\] , we get
 \[(1) \Rightarrow Dx = 25\]
Where, \[D = 5\]
Now, we get
 \[5x = 25\]
By simplify the equation, we get
 \[x = 5\]
By substituting the value \['D'\] into the equation \[(2)\] , we get
 \[(2) \Rightarrow Dy = 50\]
Where, \[D = 5\]
Now, we get
 \[5y = 10\]
By simplify the equation, we get
 \[y = 10\]
Therefore, the value of \[x = 5\] .
So, the final answer is option (D) \[5\]
So, the correct answer is “Option D”.

Note: We note that the equations and substituted values are given. Here we need to solve this simultaneous equations. The terms simultaneous and systems of equations refer to conditions where two or more unknown variables are related to each other through an equal number of equations. Applying the substitution method to systems of three or more variables involves a similar pattern, only with more work involved. This is generally true for any method of solution: the number of steps required for obtaining solutions increases rapidly with each additional variable in the system. To solve for three unknown variables, we need at least three equations.