Solve the following system of linear equations graphically and shade the region between the two lines and x-axis:
(i) 2x + 3y = 12
x – y = 1
(ii) 3x + 2y – 4= 0
2x – 3y – 7 = 0
(iii) 3x + 2y – 11 = 0
2x – 3y + 10 = 0
Answers
Given: System of linear equations:
(i) 2x + 3y = 12
y = (12 - 2x)/3…………(1)
x – y = 1
y = x - 1 ……….(2)
Solution :
For eq 1 :
When x = 0,then y = 4
When x = 6 , then y = 0
When x = 3 , then y = 2
2x + 3y = 12 passes through (0, 4) and (6, 0) , (3,2).
Plot these points on a graph paper.
For eq 2 :
When x = 0 ,then y = - 1
When x = 1 , then y = 0
When x = 3 , then y = 2
x – y = 1 passes through (0, -1) , (1, 0), (3,2).
Plot these points on a graph paper.
Two lines intersect at a point C (3,2) .
Hence x is 3 and y is 2.
(ii) 3x + 2y – 4= 0
y = (4 - 3x)/2 …………(1)
2x – 3y – 7 = 0
y = (2x - 7)/3 ……..(2)
For eq 1 :
When x = 0,then y = 2
When x = 2 , then y = - 1
When x = - 2 , then y = 5
3x + 2y – 4= 0 passes through (0,2) and (2, -1), (-2,5)
Plot these points on a graph paper.
For eq 2 :
When x = 2,then y = - 1
When x = -1 , then y = -3
When x = 5 , then y = 1
2x – 3y – 7 = 0 passes through (2, -1) , (- 1,3), (5,1).
Plot these points on a graph paper.
Two lines intersect at a point B (2,- 1) .
Hence x is 2 and y is - 1.
HOPE THIS ANSWER WILL HELP YOU……
Some more questions :
Solve the following system of equations graphically:
Shade the region between the lines and the y-axis
(i) 3x – 4y = 7
5x + 2y = 3
(ii) 4x – y = 4
3x + 2y = 14
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Solve the following systems of equations graphically:
x+y=4
2x-3y=3
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Answer:
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