**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

### Like this:

Like Loading...