Question

If 2x + 3y = 0 and 4x - 3y = 0, then x + y equals?
A) 0
B) -1
C) 1
D) 2

Answer 1

Hint: Let the given linear equations as eqn (i) and (ii) respectively. Eliminate \[y\] by adding both the equations then after solving the resulting equation to get the value of \[x\]. Substitute the value of \[x\] in one of the given equations to get \[y\]and finally put these values in the expression \[x + y\].

Complete step by step answer:
We have the given equations:-
\[2x + 3y = 0\]……………………….. (i)
\[4x - 3y = 0\]………………………… (ii)
Adding eqn (i) and eqn (ii)
We get,
\[6x = 0\]
\[ \Rightarrow x = 0\]
Substitute the value of \[x\] in equation (i) we get.
\[2 \times 0 + 3y = 0\]
\[ \Rightarrow 3y = 0\]
\[ \Rightarrow y = 0.\]
So finally, we have \[x = 0\]and also\[y = 0\]
Hence, the value of \[x + y = 0.\]

Therefore, option (a) is the correct answer.

Note:
In order to tackle such kinds of problems on linear equation in two variable one should have a basic understanding of definition for linear equation in two variables which is: An equation in the form of \[ax + by + c = 0\] where \[a,b\] and \[c\] are the real numbers, such that \[a\] and \[b\] are not both zero, is called a linear equation in two variables.
It is also recommended that to master these types of questions we will have to practice a lot of word problems on the concept of linear equations in two variables. One can also go through with the graphical approach to find the required solutions of a given linear equation by plotting the graphs on the graph sheet for his or her better understanding. One can verify the solutions whether it is correct or not we simply substitute the values of variables into each equation. For the given linear equations in this question, the graph that we plot is a straight line and on giving careful observation, we will find that graphs for both the equations are passing through the origin (0, 0).