Question

To obtain the conditions for consistency of a pair of Linear Equations in Two Variables by graphical method. A.2x – y +1 = 0 X – 2y +8 = 0 B.x – y – 5 = 0 3x – 6y – 15 = 0 C. 2x + 3y – 6 = 0 4x + 6y – 24 = 0

Answer 1

Step-by-step explanation:

Given:

A.2x – y +1 = 0, x – 2y +8 = 0

B.x – y – 5 = 0, 3x – 6y – 15 = 0

C. 2x + 3y – 6 = 0, 4x + 6y – 24 = 0

To find: To obtain the conditions for consistency of a pair of Linear Equations in Two Variables by graphical method.

Solution:

A. 2x – y +1 = 0, x – 2y +8 = 0

Ans: Find at least two-2 points of both lines

2x-y+1=0

put x=0

$2(0) - y + 1 = 0 \\ \\ - y = - 1 \\ \\ y = 1$

one point is (0,1)

Put y=0

$2x - 0 + 1 = 0 \\ \\ 2x = - 1 \\ \\ x = \frac{ - 1}{2} \\ \\ x = - 0.5$

other point is (-0.5,0)

Mark these points on graph and draw line.

x – 2y +8 = 0

put x=0

$0 - 2y + 8 = 0 \\ \\ - 2y = - 8 \\ \\ y = 4$

(0,4)

put y=0

$x - 2(0) + 8 = 0 \\ \\ x = - 8$

(-8,0)

Mark these points on same graph and draw another line.

Observe the lines, they are intersected at one point.

These lines are consistent and have unique solution.

By the same way for B and C,find the points.

Graphs for A,B and C are attached.

Final answer:

A:Consistent( unique solution)

B:Consistent( unique solution)

C: Inconsistent (No solution)

Hope it helps you.

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