Question

If \[2x + 3y = 5\] and \[3x + 2y = 10\], then the value of \[x - y = \_\_\_\_\_\_\_\_\_\]
A. 2
B. 7
C. 4
D. 5

Answer 1

Hint: In this question, we will proceed by letting the given equation as equation (1) and (2). Then subtract the equations from one another to get the required answer. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
The given equations are :
\[2x + 3y = 5...........................\left( 1 \right)\]
\[3x + 2y = 10...............................\left( 1 \right)\]
Here, we have to find the value of \[x - y\]
Now, subtract equation (1) from equation (2)
\[
   \Rightarrow \left( {3x + 2y} \right) - \left( {2x + 3y} \right) = 10 - 5 \\
   \Rightarrow 3x + 2y - 2x - 3y = 5 \\
\]
Grouping the common terms, we get
\[
   \Rightarrow x\left( {3 - 2} \right) + y\left( {2 - 3} \right) = 5 \\
   \Rightarrow x\left( 1 \right) + y\left( { - 1} \right) = 5 \\
  \therefore x - y = 5 \\
\]
Thus, the correct option is D. 5

Note: We can solve this problem by using a substitution method also. In the substitution method, we convert one of the equations in terms of only one variable by using one of its equations and then we substitute the obtained value in one of its equations to get the other value.