Question

Solve the equations graphically
2x – y = 2
4x – y = 4

Answer 1

Hint: In this question first draw the line $2x - y = 2$ on the graph then draw the line \[4x - y = 4\] on the graph and mark all the coordinates on the graph and the intersection points of these lines are the required solution, so use these concepts to reach the solution of the question.

Complete step by step solution:
Given equations are:
2x – y = 2.................. (1)
4x – y = 4.................. (2)
To draw the line ($2x - y = 2$), find out its x and y axis coordinates and simply join them.
As we know that on x-axis y = 0 and on y-axis x = 0.
So to calculate x coordinates substitute y = 0 in the equation of line we have,
$ \Rightarrow 2x - 0 = 2$
$ \Rightarrow x = \dfrac{2}{2} = 1$
So x axis coordinates = (1, 0)
Now to calculate y-axis coordinates substitute x = 0 in the equation of line we have,
$ \Rightarrow 2\left( 0 \right) - y = 2$
$y = - 2$
So y-axis coordinates = (0, -2)
So join these two coordinates as shown in the figure below by the red line.
Similarly, to draw the line (\[4x - y = 4\]), find out its x and y axis coordinates and simply join them.
As we know that on x-axis y = 0 and on y-axis x = 0.
So to calculate x coordinates substitute y = 0 in the equation of line we have,
\[ \Rightarrow 4x - 0 = 4\]
$ \Rightarrow x = 1$
So x axis coordinates = (1, 0)
Now to calculate y-axis coordinates substitute x = 0 in the equation of line we have,
\[ \Rightarrow 4\left( 0 \right) - y = 4\]
$y = - 4$
So y-axis coordinates = (0, -4)
So join these two coordinates as shown in the figure below by blue line.

So, the graphical solution of the given equations are shown in the above diagram.
The intersection point of these lines is also shown which is given as (1, 0)
So the required solution of the given lines (x, y) = (1, 0).
We can also solve this by manually
From equation 1, $y = 2x - 2$ ................. (3)
So substitute this in line 2 we have,
$ \Rightarrow 4x - \left( {2x - 2} \right) = 4$
$ \Rightarrow 4x - 2x + 2 = 4$
$ \Rightarrow 2x = 2$
$ \Rightarrow x = 1$
Now from equation (3)
$ \Rightarrow y = 2x - 2 = 2\left( 1 \right) - 2 = 0$
So the solution is (1, 0).
So this is the required answer.

Note: Whenever we face such types of questions we can solve these questions using any method (i.e. by graphically, cross multiplication method, substitution method, elimination method etc.) so here we use graphically method which is shown above and the coordinates on y-axis is found out by substituting x = 0 (because on y-axis the coordinate of x is always zero) as above in the given system of linear equation so just simplify we will get the required answer.