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Show graphically that the system of equations x – 4y + 14 = 0; 3x + 2y – 14 = 0 is consistent with unique solution. - Mathematics

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Sum

Show graphically that the system of equations x – 4y + 14 = 0; 3x + 2y – 14 = 0 is consistent with unique solution.

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Solution

The given system of equations is

x – 4y + 14 = 0 ….(1)

3x + 2y – 14 = 0 ….(2)

`x – 4y + 14 = 0 ⇒ y = \frac { x + 14 }{ 4 }`

x 6 -2
y 5 3
Points A B

`3x + 2y – 14 = 0 ⇒ y = \frac { -3x + 14 }{ 2 }`

x 0 4
y 7 1
Points C D

The given equations representing two lines, intersect each other at a unique point (2, 4). Hence, the equations are consistent with unique solution.

Concept: Graphical Method of Solution of a Pair of Linear Equations
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