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Q3.    Form the pair of linear equations for the following problems and find their solution by substitution method.

(vi) 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?

Let x be the age of Jacob and y be the age of Jacob's son, Now, According to the question  Also, Now, From (1) we have, Substituting this value of x in (2)  Substituting this value of y in (3), Hence, Present age of Jacob is 40 years and the present age of Jacob's son is 10 years.

Q3.    Form the pair of linear equations for the following problems and find their solution by substitution method.

(v)  A fraction becomes $\frac{9}{11 }$, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5 }{6}$. Find the fraction.

Let the numerator of the fraction be x and denominator of the fraction is y  Now According to the question, Also, Now, From (1) we have Substituting this value of y in (2) Substituting this value of x in (3) Hence the required fraction is

Q3.    Form the pair of linear equations for the following problems and find their solution by substitution method.

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Let the fixed charge is x and the per km charge is y. Now According to the question  And Now, From (1) we have, Substituting this value of x in (2), we have Now, Substituting this value in (3)  Hence, the fixed charge is 5 Rs and the per km charge is 10 Rs. Now, Fair For 25 km : Hence fair for 25km is 255 Rs.

Q3.    Form the pair of linear equations for the following problems and find their solution by substitution method.

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

Let the cost of 1 bat is x and the cost of 1 ball is y. Now, According to the question, Now, From (1) we have  Substituting this value of y in (2) Now, Substituting this value of x in (3) Hence, The cost of one bat is 500 Rs and the cost of one ball 50 Rs.

Q3.    Form the pair of linear equations for the following problem and find their solution by substitution method.

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Let the larger angle be x and smaller angle be y  Now, As we know the sum of supplementary angles is 180. so, Also given in the question, Now, From (2) we have,  Substituting this value in (1) Now, Substituting this value of x in (3), we get  Hence the two supplementary angles are

Q3.    Form the pair of linear equations for the following problem and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them.

Let two numbers be x and y and let bigger number is y. Now, According to the question,    And Now, the substituting value of y from (2) in (1) we get, Substituting this in (2)  Hence the two numbers are 13 and 39.

Q2.    Solve $2x + 3y = 11$ and $2x - 4y = -24$ and hence find the value of ‘$m$’ for which $y = mx + 3$.

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  Substituting this value of x in (3) Hence, Solution of the given equations is, Now, As it satisfies  , Hence Value of m is -1.

Q1.    Solve the following pair of linear equations by the substitution method.

(vi)    $\\\frac{3x}{2} - \frac{5y}{3}= - 2\\ \frac{x}{3} + \frac{y}{2} = \frac{13}{6}$

Given,    From (1) we have, Putting this in (2) we get, putting this value in (3) we get, Hence

Q1.    Solve the following pair of linear equations by the substitution method.

(v)    $\\\sqrt2x + \sqrt3y = 0\\ \sqrt3x - \sqrt8y= 0$

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  Substituting this value of x in (3) Hence, Solution of the given equations is, .

Q1.    Solve the following pair of linear equations by the substitution method.

(iv)    $\\0.2x + 0.3y = 1.3\\ 0.4x + 0.5y = 2.3$

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  Substituting this value of x in (3) Hence, Solution of the given equations is,   .

Q1.    Solve the following pair of linear equations by the substitution method.

(iii)    $\\ 3 x - y = 3\\ 9x - 3y = 9$

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  This is always true, and hence this pair of the equation has infinite solutions. As we have   , One of many possible solutions is .

Q1.    Solve the following pair of linear equations by the substitution method.

(ii)    $\\s - t = 3\\ \frac{s}{3} + \frac{t}{2} = 6$

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  Substituting this value of t in (3) Hence, Solution of the given equations is s = 9 and t = 6.

Q1.    Solve the following pair of linear equations by the substitution method.

(i)    $\\x + y = 14\\ x - y = 4$

Given, two equations, Now, from (1), we have  Substituting this in (2), we get  Substituting this value of x in (3) Hence, Solution of the given equations is x = 9 and y = 5.
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