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Pair of Linear Equations in Two Variables

Long Answer Type

191.

Draw the graph of the following equation x + y = 5, 3x - y = 3. Shade the region bounded by these lines and x-axis.

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192.

Nitish went to winter sale at Kamla Nagar to purchase some shirts and jackcts. When his friend asked him how many of each he had bought, he answered. “The number of jackets is three less than four times the number of shirts purchased. Also the number of jackets is four less than five times the numbers of shirts purchased.” Help his friends to find how many shirts and jackets Nitish bought. Express the solution graphically.

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193. Solve graphically the following system of linear equation, 2x + y = 6, x - 2y = -2. Also find the co-ordinates of the points where the lines meet the A-axis.

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194.

Represent the following pair of equations graphically and write the coordinates of points where the lines intersect y-axis :
x + 3y = 6
2x - 3y = 12

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Short Answer Type

195. Solve the following system of equation by substitution method :

$fraction numerator 3 straight x over denominator 2 end fraction minus fraction numerator 5 straight y over denominator 3 end fraction equals negative 2 straight x over 3 plus straight y over 2 equals 13 over 6$

The given equation are

$fraction numerator 3 straight x over denominator 2 end fraction minus fraction numerator 5 straight y over denominator 3 end fraction equals negative 2 space comma space space space space space space space straight x over 3 plus straight y over 2 equals 13 over 6$

$rightwards double arrow space space space space space space 9 x minus 10 y equals negative 2 cross times 6 rightwards double arrow fraction numerator 2 x plus 3 y over denominator 6 end fraction equals 13 over 6 rightwards double arrow space 9 x minus 10 y equals negative 12 space space space space rightwards double arrow 2 x plus 3 y equals 13$

Thus, we have,
9x - 10y = -12 ...(i)
2x + 3y = 13 ...(ii)
From (ii), we get

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Substitution the value of eqn. (iii) in (i). we get

9 open parentheses fraction numerator 13 minus 3 straight y over denominator 2 end fraction close parentheses minus 10 straight y equals negative 12 rightwards double arrow space space space space fraction numerator 9 left parenthesis 13 minus 3 straight y right parenthesis minus 20 straight y over denominator 2 end fraction equals negative 12 rightwards double arrow 9 left parenthesis 13 minus 3 straight y right parenthesis minus 20 straight y space equals negative 24 rightwards double arrow space 117 minus 27 straight y minus 20 straight y equals negative 24 rightwards double arrow space 117 minus 47 straight y space equals negative 24 rightwards double arrow space minus 47 straight y space equals negative 24 minus 117 rightwards double arrow space minus 47 straight y space equals negative 141 rightwards double arrow space straight y space equals space 141 over 47 equals 3

Putting the value of ‘y’ in (iii), we get

straight x space equals space fraction numerator 13 minus 3 cross times 3 over denominator 2 end fraction rightwards double arrow space space space straight x equals fraction numerator 13 minus 9 over denominator 2 end fraction equals 4 over 2 equals 2

Hence, the solution is x = 2, y = 3.

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196. Solve the following system of equation by substitution method :

square root of 2 straight x end root plus square root of 3 straight y end root equals 9 space space space space space space space space space space space square root of 3 straight x end root minus square root of 8 straight y end root equals 0 space space space space space space space space space space space

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197. A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs. 250 a quintal, the total monthly expenses of the family are Rs. 1000 and when it is 240 a quintal, the total monthly expenses are Rs. 980. Find the total monthly expenses of the family when the cost of wheat is Rs. 350 a quintal.

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198. A two digit number is obtained by either multiplying the sum of digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2. Find the number.

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199. A and B are friends and their ages differ by 2 years. A’s father D is twice as old as A and B is hvicc as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.

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200. A man sold a chair and a table together for Rs. 1520 thereby making a profit of 25% on the chair and 10% on table. By selling them together for Rs. 1535 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

2448 Views