Question

If \[15X + 17Y = 21\], \[17X + 15Y = 11\]. Then find the value of \[X - Y\]

Answer 1

Hint: The given equations are a system of simultaneous linear equations in two variables x and y.so first we have to solve the equations to get values of x and y then we can find the value of \[x - y\]. We can solve the given equations by using the Elimination Method by multiplying each equation by a suitable number so that the two equations have the same leading coefficient.

Complete step by step answer:
Consider the given system of linear equations
\[15X + 17Y = 21 - - - \left( 1 \right)\]
\[17X + 15Y = 11 - - - \left( 2 \right)\]
Now let us equate the coefficient of x equal so multiply equation 1 by 17 and equation 2 by 15
We get
\[255X + 289Y = 357\]
\[255X + 225Y = 165\]
Now subtract equation 2 from equation 1 we get
\[255X + 289Y - 255X - 225Y = 357 - 165\]
On simplification x gets canceled we get
\[ \Rightarrow 64y = 192\]
\[y = \dfrac{{192}}{{64}} = 3\]
Now to get the value of x substitute the value of y in equation 1 we get
\[15x + 17(3) = 21\]
\[ \Rightarrow 15x = 21 - 51 = - 30\]
\[ \Rightarrow x = \dfrac{{ - 30}}{{15}} = - 2\]
Therefore, the solution of the given system of equation is given by \[x = - 2\] and \[y = 3\] now we can find the value of \[x - y\] by substituting the values of x and y and is given by
\[x - y = - 2 - 3 = - 5\]

Note: The linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. We know that if a pair of definite values of two unknown quantities simultaneously satisfies two distinct linear equations in two variables, then those two equations are called simultaneous equations in two variables. There are different methods for solving simultaneous linear Equations:
Elimination of a variable
Substitution
Cross-multiplication
Graphical method
Evaluation of proportional value of variables