1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).
solution :
Let the cost of a notebook to be = ₹ x
Let the cost of a pen to be = ₹ y
According to the question,
Cost of a notebook = 2 × Cost of a pen
` \x = 2 × y\ `
` \x=2y\ `
` \x−2y = 0\ `
The cost of a notebook is twice the cost of a pen.
2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) ` \2x+3y=9.3 \overline5 \ `
(ii) ` \x-\frac{y} {5} -10=0\ `
(iii) ` \-2x+3y=6\ `
(iv) `\x=3y\ `
(v) ` \2x=-5y\ `
(vi) ` \3x+2=0\ `
(vii) `\y-2=0\ `
(viii) ` \5=2x\ `
solution :
(i) ` \2x+3y=9.3 \overline5 \ `
` \2x+3y=9.3 \overline5 \ ` can be written as ` \2x+3y-9.3\overline5=0 \ `
Now, comparing ` \2x+3y-9.3\overline5=0 \ ` with ` \ax+by+c=0 \ `
Here,
` \a=2\ `
` \b=3\ `
` \c= -9.3 \overline5 \ `
(ii) ` \x-\frac{y} {5} -10=0\ `
` \x-\frac{y} {5} -10=0\ ` can be written as ` \1x-\frac{1} {5}y -10=0\ `
Now, comparing ` \1x-\frac{1} {5}y -10=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=1\ `
` \b=\frac{1} {5}\ `
` \c= -10 \ `
(iii) ` \-2x+3y=6\ `
` \-2x+3y=6\ ` can be written as ` \-2x+3y-6=0\ `
Now, comparing ` \-2x+3y-6=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=-2\ `
` \b=3\ `
` \c= -6 \ `
(iv) `\x=3y\ `
`\x=3y\ ` can be written as ` \1x-3y+0=0\ `
Now, comparing ` \1x-3y+0=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=1\ `
` \b=-3\ `
` \c= 0 \ `
(v) ` \2x=-5y\ `
` \2x=-5y\ ` can be written as ` \2x+5y+0=0\ `
Now, comparing ` \2x+5y+0=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=2\ `
` \b=5\ `
` \c=0 \ `
(vi) ` \3x+2=0\ `
` \3x+2=0\ ` can be written as ` \3x+0y+2=0\ `
Now, comparing ` \3x+0y+2=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=3\ `
` \b=0\ `
` \c= 2 \ `
(vii) `\y-2=0\ `
`\y-2=0\ ` can be written as ` \0x+1y-2=0\ `
Now, comparing ` \0x+1y-2=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=0\ `
` \b=1\ `
` \c= -2 \ `
(viii) ` \5=2x\ `
` \5=2x\ ` can be written as ` \-2x+0y+5=0\ `
Now, comparing ` \-2x+0y+5=0\ ` with ` \ax+by+c=0 \ `
Here,
` \a=-2\ `
` \b=0\ `
` \c= 5 \ `
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