Method of Substitution to Find the Solution of a Pair of Linear Equations

Q.

$5$ pencils and $7$ pens together cost $Rs.50,$ whereas $7$ pencils and $5$ pens together cost $Rs.46.$ Find the costs of one pencil and one pen.

Q. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Q.

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. Then the number is ___.

1. 27

2. 72

3. 63

4. 36

Q. If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5. find the fraction.

Q. The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Q.

A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.

Q.

Reena has. Pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens . Find original number of pens and pencils.

Q.

Father's age is 3 times the sum of Ages of his two children . after 5 years his age will be twice the sum of Ages of two children find the age of father

Q.

How do you solve linear equations in three variables?

Q.

Solve for x and y:

$2x+3y=0,3x+4y=5.$

Q.

Five years hence, the age of jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Q.

The sum of a 2 digit number and the number formed by interchanging the digit is 110.If 10 is subtracted from the first , the new number is 4 more than 5 times the sum of the digits in the first number .Find the first number

Q. The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction. ​

1. $\frac{5}{9}$
2. $\frac{9}{5}$
3. $\frac{3}{7}$
4. $\frac{7}{3}$

Q.

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.

Q.

The sum of two numbers is 16 and the sum of their reciprocals is $\frac{1}{3}$.Find the numbers.

Q.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find the angles. [3 MARKS]

Q.

Two years ago, a man was five times as old as his son.Two years later, his age will be 8 more than three times the ages of his son.Find the present ages of the man and his son.

Q.

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Q.

A two-digit number is such that the product of its digits is 18.If 63 is subtracted from the number, the digits interchange their places.Find the number.

Q.

the sum of a two digit number and the number obtained by reversing the digits is 66 if the digit of the number differ by 2 find the number how many such numbers are there?

Q. Question 16
Two years ago, Salim was thrice as old as his daughter and six years later he will be four year older than twice her age. How old are they now?

Q.

If twice the son's age in years is added to the father's age, the sum is 70. But, if twice the father's age is added to the son's age, the sum is 95. Find the ages of father and son.

Q.

A number consisting of two digits is seven times the sum of its digits.When 27 is subtracted from the number, the digits are reversed.Find the number.

Q.

The present age of a woman is 3 years more than three times the of her daughter.Three years hence, the woman's age will be 10 years more than twice the age of her daughter.Find their present ages.

Q. Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.

Q.

The sum of two numbers is 137 and their difference is 43.Find the numbers.

Q. If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

Q. A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 liters of a 40% acid solution? [ 4 MARKS]

Q. Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B?

Q.

In a given fraction, if 1 is subtracted from the numerator and 2 is added to the denominator, it becomes $\frac{1}{2}$.if 7 is subtracted from the numerator and 2 is subtracted to the denominator, it becomes $\frac{1}{3}$.The fraction is

(a) $\frac{13}{24}$ (b) $\frac{15}{26}$ (c) $\frac{16}{27}$ (d) $\frac{16}{21}$