Graphical Method of Finding Solution of a Pair of Linear Equations
To solve the pair of linear equation proceed as below.
Step 1: Draw a graph for each linear equation.
Step 2: Find the coordinate of the point of intersection of the two drawn lines.
Step 3: The coordinates of the point of intersection of the lines are the solutions of given linear equations.
>> If the lines are intersecting.
Intersecting lines have one common point. So, the pair of linear equation will have one solution.
>> If the lines are parallel.
Parallel lines have no common points. So, the pair of linear equations will have no solution.
>> If the lines are coincident.
Coincident lines have infinite common points. So, the pair of equations will have infinitely many solutions.
Q.1. Solve each of the following systems of equations graphically:
(i) 3x+2y=4, 2x-3y=7
(ii) 3x+y+1=0, 2x-3y+8=0
(iii) x+2y+2=0, 3x+2y-2=0
(iv) 2x+3y=8, x-2y+3=0
Q.2. Solve the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
(i) x-y+1=0, 3x+2y-12=0
(ii) x-2y+2=0, 2x+y-6=0
Q.3. Show graphically that each of the following given systems of equations has infinitely many solutions:
(i) x – 2y = 5, 3x – 6y = 15
(ii) 2x + 3y = 6, 4x + 6y = 12
Q.4. Show graphically that the following given systems of equations is inconsistent, i.e., has no solution.
2x+3y=4, 4x+6y=12
Q.5. Solve the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis.
2x-5y+4=0, 2x+y-8=0
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