Solve the following system of linear equations graphically:

Q) Solve the following system of linear equations graphically:

3 x – y + 1 = 0

x + y = 5

Ans:

Step 1: To plot the equations, let’s first find out the coordinates of points lying on these lines:

For line: 3 x – y + 1 = 0,, we calculate coordinates of various points:

at X = 0, 3 (0) – y + 1 = 0 ∴ y = 1

at X = 1, 3 (1) – y + 1 = 0 ∴ y = 4

at Y = 0, 3 x – 0 + 1 = 0 ∴ x = $\frac{- 1}{3}$

at Y = 2, 3 x – 1 + 1 = 0 ∴ x = $\frac{1}{3}$

Hence, we get the following table:

$\begin{tabular}{ |c|c|c|c| } \hline 0 & 1 & - 1/3 & 1/3 \\ \hline 1 & 4 & 0 & 2 \\ \hline \end{tabular}$

Similarly for line: x + y = 5, we calculate coordinates of various points:

at X = 0, (0) + y = 5 ∴ y = 5

at X = 1, (1) + y = 5 ∴ y = 4

at Y = 0, x + 0 = 5 ∴ x = 5

at Y = 1, x + 1 = 5 ∴ x = 4

Hence, we get the following table:

$\begin{tabular}{ |c|c|c|c| } \hline 0 & 1 & 5 & 4 \\ \hline 5 & 4 & 0 & 1 \\ \hline \end{tabular}$

Step 2: Now let’s plot both of these lines connecting each of the points:

From the diagram, we can see that the lines intersect each other at point (1, 4)

Therefore, the solution of the lines is (1, 4).

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