NCERT Class 9 Solution: Linear Equation In Two Variables (Chapter 4) Exercise 4.1

Line ax+by+c = 0 on the coordinate plane

Equaltion of a Line Plotted on the Coordinate Plane

Line ax+by+c = 0 on the coordinate plane

Q-1 The cost of a notebook is twice the cost of a pen. Write a linear equation in two variable to represent this statement.

(Take the cost of a notebook to be Rs x and that of a pen to be Rs y. )

Solution:

Consider the cost of a notebook be x and that of a pen be y .

A linear equation has to equate the two things. According to question, the cost of a notebook is twice the cost of a pen

So, x=2y

Therefore, linear equation becomes,

x2y=0 .

Q-2 Express the following linear equations in the form ax+by+c=0 and indicate the value of a,bandc in each case:

  1. 2x+3y=9.35¯

  2. xy510=0

  3. 2x+3y=6

  4. x=3y

  5. 2x=5y

  6. 3x+2=0

  7. y2=0

  8. 5=2x

Solution:

  1. 2x+3y=9.35¯

    • So, 2x+3y9.35¯=0

    • Compare, the equation with ax+by+c=0

    • Therefore, value of a,b and c is a=2,b=3,c=9.35¯

  2. xy510=0

    • Compare the equation with ax+by+c=0 .

    • Therefore, a=1,b=15,c=10 .

  3. 2x+3y=6

    • So, 2x+3y6=0

    • Compare, the equation with ax+by+c=0

    • Therefore, a=2,b=3,c=6

  4. x=3y

    • So, x3y=0

    • Compare, the equation with ax+by+c=0

    • Therefore, a=1,b=3,c=0

  5. 2x=5y

    • So, 2x+5y=0

    • Compare, the equation with ax+by+c=0

    • Therefore, a=2,b=5,c=0

  6. 3x+2=0

    • Compare, the equation with ax+by+c=0

    • Therefore, a=3,b=0,c=2

  7. y2=0

    • Compare, the equation with ax+by+c=0

    • Therefore, a=0,b=1,c=2

  8. 5=2x

  • So, 2x5=0

  • Compare, the equation of ax+by+c=0

  • Therefore, a=2,b=0,c=5

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