Question

Solve the following system of linear equations graphically: 2x — 3y = 1, 3x — 4y = 1 Does the point (3, 2) lie on any of the lines? Write its equation.

Answer 1

Topic - Linear Equations

The linear equations are

• 2x - 3y = 1 .....(i)
• 3x - 4y = 1 .....(ii)

For equation (i), we find a set of points:

$\quad$$\begin{array}{|ccccc|} \cline{1-5}x& \to &2&5&-1\\ \cline{1-5}y& \to &1&3&-1\\ \cline{1-5}\end{array}$

$\quad$We plot the points (2, 1), (5,3) and (- 1, - 1) on paper and draw the straight line for equation (i).

For equation (ii), we find a set of points:

$\quad$$\begin{array}{|ccccc|} \cline{1-5}x& \to &3&7&-1\\ \cline{1-5}y& \to &2&5&-1\\ \cline{1-5}\end{array}$

$\quad$We plot the points (3, 2), (7, 5) and (- 1, - 1) on paper and draw the straight line for equation (ii).

Finding their point of intersection:

$\quad$We find that the common point or the point of intersection is (- 1, - 1).

Therefore the required solution is

$\quad\quad$x = - 1, y = - 1

Also, we see that the point (3, 2) lies on the second straight line 3x - 4y = 1.

Answer 2

Answer:

Here is your answer.

Step-by-step explanation:

There are four pictures

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