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Pair Of Linear Equation

The Level 2 of the Pair Of Linear Equation in two variable of study material consists of the questions like solving of equations using cross multiplication method , finding the fractions....etc.


1. 5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of on pencil and that of one pen.

Solution:-

         Let number of pencils be x
               number of pens be y 

         Then,

                                5x + 7y = 50        -----------(1)

                                7x + 5y = 46        -----------(2)

         (1)*7 , We get ,

                                35x + 49y = 350   ----------(3)  

         (2)*5 , We get ,

                                35x + 25y = 230   ----------(4)

         Solving (3) and (4)

                                35x + 49y = 350

                                35x + 25y = 230
                              (-)    (-)        (-)
                            ___________________

                                        24y = 120
                                           y = 5

         Plug the value of y in (1)

                                5x + 7y = 50
                                5x + 35 = 50
                                5x = 15
                                x = 3

Therefore the cost of one pencil is Rs. 3 and cost of one pen is Rs.5 .

pair of linear equation

2. Solve the equations:

                              3x - y = 3
                              7x + 2y = 20

Solution:-

                              3x - y = 3            -----------(1)
                              7x + 2y = 20        -----------(2)

(1)*3 , We get,

                             6x - 2y = 6           -----------(3)

(2)+(3), We get,

                              7x + 2y = 20
                              6x - 2y = 6
                            (+)   (-)        (+)
                                  _________________

                                     13x = 26
                                     x = 2

Now we have to plug the x value in (1), We get,

                             3x - y = 3
                             3(2) - y = 3
                             6 - y = 3
                             -y = 3-6
                             y = 3

Therefore x = 2 and y = 3.

pair of linear equation

3. Find the fraction which become to 2/3 when the numerator is increased by 2 and equal to 4/7 when the denominator is increased by 4.

Solution:-

             Let the fraction by \(\frac{x}{y}\) .

             Then in the Case 1,

                            \(\frac{x+2}{y} = \frac{2}{3}\)  

                            3(x+2) = 2y

                            3x - 2y = -6                      ---------(1)
             In Case 2,

                            \(\frac{x}{y+4} = \frac{4}{7}\)  

                            7x = 4(y+4)

                            7x - 4y = 16                       ---------(2)

            (1)*2, We get, 

                            6x - 4y = -12                    ---------(3)

             (2)-(3), We get,

                            7x - 4y = 16
                            6x - 4y = -12
                           (-)   (+)       (+)
                       ________________
                            x = 28

             Plug the value of 'x' in (1),

                           3(28) -  2y = -6
                           84 - 2y = -6
                           -2y = -90
                           y = 45

Therefore the fraction is \(\frac{28}{45}\) .

4. Solve the equation:

                          px + qy = p - q
                          qx - py = p+q

Solution:-

             Let us use cross multiplication method.

               x                  y             1
        q          -(p-q)            p              q

        -p        -(p+q)            q             -p

                     \(\frac{x}{-qp-q^2-(p^2-pq)}\) = \(\frac{y}{-pq+q^2-(-p^2-pq)}\) = \(\frac{1}{-p^2-q^2}\)

                     \(\frac{x}{-pq+pq-q^2-p^2} = \frac{1}{-p^2-q^2}\)

                     x = \(\frac{-q^2-p^2}{-q^2-p^2}\)

                     x = 1

                     \(\frac{y}{-pq+q^2-(-p^2-pq)} = \frac{1}{-p^2-q^2}\)

                                \(\frac{y}{-pq+pq+q^2+p^2} = \frac{1}{-p^2-q^2}\)

                                y = \(\frac{q^2+p^2}{-(p^2+q^2)}\)

                     y = -1

Therefore x = 1 and y = -1.   

We provided all the solutions provided in the math study material the solutions for the questions of Pair Of Linear Equation in two variable.

To go to the Level 3 click on NEXT button.

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