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Mathematics

Solve graphically, the simultaneous equations : 2x - 3y = 7; x + 6y = 11.

Coordinate Geometry

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Answer

Given,

⇒ 2x - 3y = 7

⇒ 3y = 2x - 7

⇒ y = 2x−73\dfrac{2x - 7}{3} ………(1)

When, x = -1, y = 2×−1−73=−2−73=−93\dfrac{2 \times -1 - 7}{3} = \dfrac{-2 - 7}{3} = -\dfrac{9}{3} = -3,

x = 2, y = 2×2−73=4−73=−33\dfrac{2 \times 2 - 7}{3} = \dfrac{4 - 7}{3} = -\dfrac{3}{3} = -1,

x = 5, y = 2×5−73=10−73=33\dfrac{2 \times 5 - 7}{3} = \dfrac{10 - 7}{3} = \dfrac{3}{3} = 1.

Table of values of equation (1) :

x-125
y-3-11

Steps of construction :

  1. Plot the points (-1, -3), (2, -1) and (5, 1) on graph.

  2. Join the points.

Given,

⇒ x + 6y = 11

⇒ 6y = 11 - x

⇒ y = 11−x6\dfrac{11 - x}{6} ……….(2)

When x = -7, y = 11−(−7)6=186\dfrac{11 - (-7)}{6} = \dfrac{18}{6} = 3,

x = -1, y = 11−(−1)6=126\dfrac{11 - (-1)}{6} = \dfrac{12}{6} = 2,

x = 5, y = 11−56=66\dfrac{11 - 5}{6} = \dfrac{6}{6} = 1.

Table of values of equation (2) :

x-7-15
y321

Steps of construction :

  1. Plot the points (-7, 3), (-1, 2) and (5, 1) on graph.

  2. Join the points.

Solve graphically, the simultaneous equations : 2x - 3y = 7; x + 6y = 11. Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

From graph,

The two lines intersect at P(5, 1).

Hence x = 5, y = 1.

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