# SOLVING LINEAR EQUATIONS BY GRAPHING

## About "Solving Linear Equations by Graphing"

Solving Linear Equations by Graphing :

Here we are going to see some example problems on graphing linear equations in two variables by graphing method.

## Solving Linear Equations by Graphing - Practice questions

Question 1 :

Solve graphically

x + y = 7; x − y = 3

Solution :

x + y = 7  ----- (1)

x − y = 3  ------(2)

From (1), y = 7 - x

By giving some random values of x, we get the values of y.

So the points on the first line are (-1, 8) (0, 7) and (1, 6).

From (2),

y  =  x - 3

The points (-1, -4) (0, -3) and (1, -2) are in the second line.

By plotting the set of points from the above tables, we get the graph. The point of intersection of the given lines will be the solution.

Hence the solution is (5, 2).

Question 2 :

3x + 2y  =  4, 9x + 6y - 12  =  0

Solution :

3x + 2y  =  4  --------(1)

9x + 6y  =  12 --------(2)

From (1)  ==>  2 y  =  4 - 3x

y  =  (4 - 3x)/2

y  =  2 - (3x/2)

From (2) ==>  6y  =  12 - 9x

y  =  (12 - 9x)/6

y  =  (12/6) - (9x/6)

y  =  2  - (3x/2)

Since both lines are same, it has infinitely many solution.

Question 3 :

(x/2) + (y/4)   =  1

(x/2) + (y/4)  =  2

Solution :

Since the coefficients of x and y are same, they are parallel lines. Hence they have no solution.

Question 4 :

x - y  =  0, y + 3  =  0

Solution :

x - y  =  0  ----(1)

y + 3  =  0 -----(2)

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

From (2)  ==>  y  =  -3

Hence the solution is (-3, -3).

Question 5 :

y = 2x + 1

y + 3x - 6  =  0

Solution :

y = 2x + 1  ----(1)

y + 3x  =  6  ----(2)

From (1),

y  =  2x + 1

The point lies on the first line will be (-1, -1) (0, 1) and (1, 3).

From (2)  ==>  y + 3x  =  6

y  =  6 - 3x

Hence the solution is (1, 3).

Question 6 :

x  =  -3 and  y  =  3

Solution :

Hence the solution is (3, 3).

Question 7 :

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

Solution :

If they travel in the same direction:

Distance = Speed x Time

Car A = 2x miles

Car B = 2y miles

Total distance is 100 miles

x + y  =  100  ----(1)

They meet after 2 hours

2x  =  2y + 100

x  =  y + 50

y  =  x - 50  -----(2)

from (1), we get

x + y  =  100

y  =  100 - x

From (2),

y  =  50 - x

Hence the speed of car A is 75 km/hr and speed of car B is 25 km/hr.

After having gone through the stuff given above, we hope that the students would have understood, "Solving Linear Equations by Graphing"

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