Question

solve by using cross multiplication method 3x+4y=10 and 2x-2y=2 [class 10]

Answer 1

Answer:  The required solution of the given system is

x = 2  and  y = 1.

Step-by-step explanation:  We are given to solve the following system of equations by using the method of cross-multiplication :

$3x+4y=10\\\\\Rightarrow 3x+4y-10=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-2y=2\\\\\Rightarrow 2x-2y-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

The table of cross-multiplication is as follows :

                 x                        y                       1

4                           -10                      3                        4

-2                           -2                       2                       -2

By cross-multiplying the coefficients, we get

$\dfrac{x}{4\times(-2)-(-10)\times(-2)}=\dfrac{y}{(-10)\times2-3\times(-2)}=\dfrac{1}{3\times(-2)-4\times2}\\\\\\\Rightarrow \dfrac{x}{-8-20}=\dfrac{y}{-20+6}=\dfrac{1}{-6-8}\\\\\\\Rightarrow \dfrac{x}{-28}=\dfrac{y}{-14}=\dfrac{1}{-14}\\\\\\\Rightarrow x=\dfrac{-28}{-14}=2,~~~~~y=\dfrac{-14}{-14}=1.$

Thus, the required solution of the given system is

x = 2  and  y = 1.