Question

Draw the graph of (i) 2y – x = 9 (ii) 2x – 3y = 15
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Answer 1

Answer:-

(See the Attachment For Graph)

More To Know:-

If in a pair of linear equation say,

$\\ \tt\mapsto ax^2+bx = c.$

$\\ \tt\mapsto a_2x^2+b_2x = c_2.$

• $\tt\dfrac{a}{a_2}\neq\dfrac{b}{b_2}$ then the equations will have only one common solutions and their graph will represent two intersecting line.

• $\tt\dfrac{a}{a_2} = \dfrac{b}{b_2}\neq\dfrac{c}{c_2}$ then the equations will have no common solutions and their graph will represent two parallel lines.

• $\tt\dfrac{a}{a_2} = \dfrac{b}{b_2} = \dfrac{c}{c_2}$ then the equation will have infinite solutions and their graph will represent two lines overlapped over each other.

So in this case:-

• $\tt\dfrac{a}{a_2} = -\dfrac{2}{3}.$

• $\tt\dfrac{b}{b_2} = -\dfrac{1}{2}.$

• $\tt\dfrac{c}{c_2} = -\dfrac{9}{15}.$

Clearly,

$\\ \bf\mapsto-\dfrac{2}{3}\neq-\dfrac{1}{2}.$

And hence the equation will have only one solution and the graph will represent two intersecting lines.