Question

Solve the following pair of linear equation using cross multiplication method 5 x minus 3 y is equals to 2 and 4 x + 7 y is equals to minus 3

Answer 1

Answer:

$x = \frac{ - 30}{47} \\ \\ y = \frac{ - 23}{47}$

Given:-

$5x - 3y = 2 \\ 4x + 7y = - 3$

now for cross multiplication method

we chnge the equation

$5x - 3y - 2 = 0 \\ \\ 4x + 7y + 3 = 0$

for cross multiplication method

plz refere the picture

here,

$a_{1} = 5 \\ a_{2} = 4 \\ b_{1} = - 3 \\ b_{2} = 7 \\ c_{1} = - 2 \\ c_{2} = 3$

$\frac{x}{ b_{1} c_{2} - b_{2} c_{1} } = \frac{y}{ c_{1} a_{2} - c_{2}a_{1} } = \frac{1}{a_{1}b_{2} - \:a_{2}b_{1}} \\ \\ now \: put \: all \: the \: value$

$\frac{x}{ - 3 \times 3 - 7 \times 3} = \frac{y}{ - 2 \times 4 - 3 \times 5} = \frac{1}{5 \times 7 - 4 \times - 3} \\ \\ \frac{x}{ - 9 - 21} = \frac{y}{ - 8 - 15} = \frac{1}{35 - ( - 12)} \\ \\ \frac{x}{ - 30} = \frac{y}{ - 23} = \frac{1}{47} \\ \\ \frac{x}{ - 30} = \frac{1}{47} \\ \\ 47x = - 30 \\ \\ x = \frac{ - 30}{47} \\ \\ \frac{y}{ - 23} = \frac{1}{47} \\ \\ 47y = - 23 \\ \\ y = \frac{ - 23}{47}$

Answer 2

Solution to the pair of linear equation using cross multiplication method is

$x=\frac{5}{47},y= \frac{-23}{47}$

• Given equations can be rewritten as

                  5x - 3y - 2 = 0 ---------------(1)

                  4x + 7y + 3 = 0 --------------(2)

• Here,

                   $a_{1}=5,b_{1}=-3,c_{1}=-2$

                   $a_{2}=4,b_{2}=7,c_{2}=3$

• We know that by cross multiplication method,

                   $x=\frac{b_{1}c_{2}-b_{2}c_{1} }{a_{1}b_{2}-a_{2}b_{1}},y=\frac{c_{1}a_{2}-a_{2}c_{1} }{a_{1}b_{2}-a_{2}b_{1}}$

• Substituting values in x and y, we get

                  $x=\frac{(-3)(3)-(7)(-2) }{(5)(7)-(4)(-3)},y=\frac{(-2)(4)-(3)(5) }{(5)(7)-(4)(-3)}$

                  $x=\frac{-9+14}{35+12},y=\frac{-8-15}{35+12}$

                  $x=\frac{5}{47},y= \frac{-23}{47}$