LINEAR EQUATION
Question. In a village primary school enrolment of girls has doubled this year as compared to last year. Considering this year’s enrolment as ‘y’ and previous year’s enrollment as x :
(a) Form a linear equation for this information.
(b) If previous year’s enrolement was 35 find this year’s enrollment.
(c) What is the value depicted here ?Answer: (a) y=2x
(b) y=2×35=70
(c) Freedom, Gender equality.
Question. On her birthday Sonia distributed chocolates in an orphanage. She gave 5 chocolates to each child and 20 chocolates to adults. Taking number of children as x and total chocolates distributed as y.
(a) Form a linear equation.
(b) If she distributed 145 chocolates how many children are there in the orphanage ?
(c) Explain the value depicted here by Sonia.Answer: (a) y=5x+20
(b) 145=5x+20
= 125=5x
= x=25
(c) Happiness, Helpfulness
Question. In a housing society people decided to do Rainwater harvesting. Rainwater is collected in the underground tank at the rate of 30 cm³/ sec. Taking volume of water collected in x sec as y cm³.
(a) Form a linear equation.
(b) Write it in standard form as ax+by+c=0.
(c) Which value is promoted by the members of this society ?Answer: (a) y=30x
(b) 30x–y+0=0
(c) Environmental protection, Co-operation.
Question. Aman hires an auto rickshaw to cover a certain distance. The fare is Rs. 10 for first km and Rs. 7 for subsequent kilometers. Taking total distance covered as x km and total fare as y :
(a) Write a linear equation for this.
(b) The man covers a distance of 16 kmand gave Rs. 120 to the auto driver.Auto driver said ‘‘It is not the correct amount’’and returned him the balance. Find the correct amount paid back by the autodriver.
(c) Which value is depicted here by the autodriver ?Answer: (a) y=10+7(x–1)
=10+7x–7
y=7x+3
(b) y=7×16+3
=112+3=115 Rs. Amt. Paid back = 120–115 = 5 Rs.
(c) Honesty, Truthfulness.
Question. In a ‘‘Cleanliness drive’’ residents of certain locality joined together to clean neighbourhood area. Participation of children was 20 more than that by adults. Taking x as number of adults and y as number of children.
(a) Form a linear equation.
(b) What values are depicted here ?Answer: (a) y=x+20
(b) Co-operation, Happiness, Sincerity, Environmental protection.
Question. Rehman and Prakash together contributed Rs. 500 towards Prime Minister Relief fund.
(a) Write the linear equation for this.
(b) Write the values involved in it.Answer: (a) x+y=500
(b) Co-operation, Helpfulness
Question. Draw the graph of the linear equation 2(x+1)=3(y–1)–4 and check whether point (–3, +1) lies on the line ?
Which value is depicted here ?Answer: (a) Equation
2(x+1)=3(y–1)–4
=2x+2=3y–3–4
=2x–3y+9=0
Point (–3, +1) lies on it as
2×(–3)–3(+1)+9 = –6 – 3+9
= –9 + 9 = 0 = RHS.
(b) Curiosity, Truthfulness, Scientific temper.
Question. In a class, teacher asked about the equ. of line passing through the origin with options as :
y+x=1, x+3y=2, x+y=0
Rehana answered it correctly as x+y=0.
Choose the correct value :
(a) Honesty (b) Equality (c) Truthfulness (d) Sincerity
Answer: (c) Truthfulness
Question.
(a) In the above fig. (i) & (ii) find the values of a & b.
(b) Is a=b ? Justify your answer.
(c) What is the value depicted here ?Answer: (a) a=3, b=3
(b) Yes
(c) Scientific temper, Truthfulness, Knowledge.
Question. (a) Every six months price of petrol increases at the rate of Rs. 4 per litre. Taking price of petrol in Dec. 2011 as ‘x’ and present price of petrol as ‘y’ form a linear equation showing amount spent on petrol in Dec. 2012.
(b) Due to continuous rise in the petrol price people are shifting towards CNG in place of petrol whose price increases at a rate of Rs. 3 per litre in a year. Form a linear equation taking price of CNG in Dec. 2011 as ‘a’ and in Dec. 2012, as ‘b’.
(c) Which fuel will you prefer and why ?
(d) Which value is depicted by using CNG over petrol ?
Answer: (a) y=x+8
(b) b=a+3
(c) CNG, because CNG is cheaper than petrol.
(d) Environmental protection.
