Question

How do you find the intersection of two lines?

Answer 1

Hint: Now to find the intersection of the line we will first try to plot both the lines on a graph paper. To plot the lines we must find the points $\left( x,y \right)$ which satisfies the lines. To do so we will write y in terms of x and substitute different values of x and find the corresponding values of y. Hence we will plot these points $\left( x,y \right)$ . Now we will draw a line passing through the points obtained. Hence we will draw both the lines and find the intersection point of the line.

Complete step by step solution:
Now first let us understand the equation of a line.
Equation of a line is a linear equation in two variables. Which means the highest power of both the variables is 1.
Now to find the intersection of the line we will first try to plot the lines on a graph.
Now to plot a line on a graph we will rearrange the equation such that we have y in terms of x. Now we will substitute different values of x to find corresponding values of y. Hence we have the pair $\left( x,y \right)$ which satisfies the solution. Now find the minimum of two such points and plot them on a graph paper. Now draw a line passing through these points and hence we have the geometric representation of the line. Now similarly we will draw the other line and hence find the intersection point of the line.
Hence we have the intersection of the given line.

Note: Now note that we can also solve this with algebraic method. To do so let us consider any one equation of line. Now rearrange the equation to write y in terms of x. Now substitute this value of y in another equation. Hence now we have a linear equation in x. We will solve this equation to find the value of x. Now substitute the value of x in the equation to find the value of y. Hence we have the solution of the given equation.