**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).

## Properties of a straight line

### Step 1 :

#### Equation of a Straight Line

1.1 Solve 4x-3y = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 4x-3y = 0 and calculate its properties

#### Graph of a Straight Line :

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 0/-3 so this line "cuts" the y axis at y=-0.00000

y-intercept = 0/-3 = -0.00000#### Calculate the X-Intercept :

When y = 0 the value of x is 0/4 Our line therefore "cuts" the x axis at x= 0.00000

x-intercept = 0/4 = 0.00000#### Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.000 and for x=2.000, the value of y is 2.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.667 - 0.000 = 2.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 2.667/2.000 = 1.333### Geometric figure: Straight Line

- Slope = 2.667/2.000 = 1.333
- x-intercept = 0/4 = 0.00000
- y-intercept = 0/-3 = -0.00000

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## 3y 0 4x

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