Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { l }
x - y = 1 \
2 x - 3 y = - 4
\end{array}$

Question

Draw the graphs of the pair of linear equations. Find the point of intersection. If the lines do not intersect, tell whether the lines are parallel or coincide. $\begin{array} { l } 
x - y = 1 \
2 x - 3 y = - 4
\end{array}$

Quizplus · Accepted Answer

The given pair of linear equations are:
$$x-y=1$$
$$2x-3y=-4$$

To draw the graph of a linear equation, we need to find its two or more solution points by giving arbitrary values to any one variable and then calculating the value of the other variable.

The solution points of the first equation are given below:

Let x = 0, then y = -1.

Let y = 0, then x = 1.

So, the solution points are (0, -1) and (1, 0).

The solution points of the second equation are given below:

Let x = 0, then y = 4/3.

Let y = 0, then x = -2.

So, the solution points are (0, 4/3) and (-2, 0).

Now, we can plot these solution points on the coordinate axes and draw the lines passing through them.

The graph of the first equation is a straight line passing through (0, -1) and (1, 0), as shown below:

11ec0955_fa14_3083_a41c_f82d3bfa628a_TBX8813_11

The graph of the second equation is a straight line passing through (0, 4/3) and (-2, 0), as shown below:

11ec0955_fa14_3084_a41c_6c82f545282d_TBX8813_11

The point of intersection of these two lines is (1, 0), which can be found either by solving the system of equations or by inspecting the graphs.

Therefore, the solution of the system of equations is (1, 0).

Hence, the answer is A).

Draw the Graphs of the Pair of Linear Equations x−y=12x−3y=−4\begin{array} { l } x - y = 1 \\2 x - 3 y = - 4\end{array}x−y=12x−3y=−4​

Draw the Graphs of the Pair of Linear Equations $\begin{array} { l } x - y = 1 \\2 x - 3 y = - 4\end{array}$