Question

Find values of x and y if (5x - 3y, y - 3x) = (2, 1)

Answer 1

★Given:-

• (5x - 3y, y - 3x) = (2, 1)

★find:-

• value of x and y

★SOLUTION:-

$\implies \: ( \red{5x - 3y}, \pink{y - 3x}) = ( \red{2}, \pink{1})$

we see that

$\implies \red {5x - 3y = 2} - - - (1)$

and

$\implies \pink{y - 3x = 1}$

take - common

$\implies \pink{ - (3x - y) = 1}$

$\implies \pink{3x - y = - 1} - - - (2)$

EQ (2) multiplie by 3

$\implies \pink{9x - 3y = - 3} - - - (3)$

now subscrate equition (2)-(1) to we get

$\implies \: 9x - 3y - (5x - 3y) = - 3 - 2 \\ \\ \implies \: 9x - 5x \cancel{- 3y }+ \cancel{3y }= - 5 \\ \\ \implies \: 4x = - 5 \\ \\ \implies \boxed{ x = \frac{ - 5}{ \: \: \: \: 4} }$

x value put on EQ (1)

$\implies \: 5( \frac{ - 5}{ \: \: \: 4} ) - 3y = 2 \\ \\ \implies \: 3y = - \frac{25}{4} - 2 \\ \\ \implies \: 3y = \frac{ - 25 - 8}{4} \\ \\ \implies \: y = \frac{ - \cancel{33}}{4 \times \cancel3} \\ \\ \implies \boxed{ y = - \frac{11}{4} }$

therefore:-

• value of x=-5/4

• value of y=-11/4

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I hope it helps you