Question

Solve graphically, the following pairs of equations:
$2x+y=23$
$4x-y=19$
A. $x=1,y=4$
B. $x=9,y=2$
C. $x=5,y=0$
D. $x=7,y=9$

Answer 1

Hint: To find the solution of the following pairs of linear equations, we will draw the graph for each of the equations and look for a point of intersection between the graph of two lines. The coordinates of point of intersection would be the solution of the system of linear equations.


Complete step by step answer:
The above question demands that we have to solve the following system of linear equations graphically. A system of linear equations is just a set of two or more linear equations in two or more than to variables. Thus, we are going to see step by step how we can solve a system of linear equations of two variables graphically. First, we are going to find y in terms of x in both the equation above. After doing this we will get: -
$y=23-2x$ ……………………….(i)
$y=4x-19$ ……………………..(ii)
Now, we are going to find different values of y in the above equations by putting different values of x. First, we are going to do this for equation (i).
For equation (i)
Let the value of x be 10, then after putting this value of x in equation (i), we get the value of y as follows: -
$\Rightarrow y=23-2\left( 10 \right)$
$\Rightarrow y=23-20$
$\Rightarrow y=3$
Here, we consider this as point $A\left( 10,3 \right)$
Now, let us take the value of x as 9, then after putting this value of x in equation (ii), we get the value of y as follows:
$\Rightarrow y=23-2\left( 9 \right)$
$\Rightarrow y=23-18$
$\Rightarrow y=5$
Here, we get the point $B\left( 9,5 \right)$
We will now try to obtain the points similarly for the equation (ii). Thus, now if $x=5$ we will get $y=1$. We will name this as $A'\left( 5,1 \right)$. Also, if $x=6$ we will get $y=5$. This point is $B'\left( 6,5 \right)$. Now, we will plot the graph for two lines on a graph paper and we have to find an intersection point.

Thus, we can clearly see that the intersection point of the two lines is $O\left( 7,9 \right)$. Thus, the answer of this question will be $x=7$ and $y=9$.
Hence, option (d) is correct.

Note:
To check whether the intersection point we found out through graphical method is correct or not, we will put the value of $x=7$in both the equations we will get the value of $y=9$ in both the cases. If values are not matching then there is some error in the points we found.