Question

Solve the graphically 2x-y-5=0,2x+y-6=0

Answer 1

Solution :

❈ Step 1 :

The equations are

    2x - y - 5 = 0 ...(i)

    → 2x - y = 5

    → $\frac{2x}{5}+\frac{-y}{5}=1$

    → $\dfrac{x}{\frac{5}{2}}+\frac{y}{-5}=1$

Line (i) intersects x axis at $(\frac{5}{2},0)$ and y axis at (0, - 5)

    2x + y - 6 = 0 ...(ii)

    → 2x + y = 6

    → $\frac{2x}{6}+\frac{y}{6}=1$

    → $\frac{x}{3}+\frac{y}{6}=1$

Line (ii) intersects x axis at (3, 0) and y axis at (0, 6)

❈ Step 2 :

Now, draw a set of rectangle axis XOX' and YOY'

Plotting the set of points for each lines and connecting the respective points, we get two intersecting lines.

❈ Step 3 :

From the graph, it can be found easily that the point of intersection of the given two lines is $(\frac{11}{4},\frac{1}{2})$.

❈ Step 4 :

Therefore, the required solution be

  $\boxed{\mathsf{x = \frac{11}{4}\:\:and\:\:y=\frac{1}{2}}}$

Answer 2

This question is asked repeated in SSC Boards for 5 or 6 Marks. Question can be solved easily. But, Presentation is very important. I am proving the answer in the necessary format.

Given System of equations :

2x-y-5=0,2x+y-6=0

Procedure :

1) Take various values of x to get various values of y.

2) Now, Plot them on the graph.

3) The solution of the lines is intersection of both lines.

4) Graph must be prepared to have a scale ; which should be followed by labeling the points continously.

For the first equation,

2x - y - 5 = 0.

y = 2x - 5

For the second equation,

2x+y-6=0

- (2x - 6) = y

y = 6 - 2x

Now.., We get the table as shown.

From the graph, We would get that two lines meet at 11/4, 1/2 which is the required solution.