Question

Solve following pair of linear equations using cross multiplication method 5x-3y=2 4x+7y=-3

Answer 1

heya mate

hope it helps you

Answer 2

$\boxed{\huge{\bf{\pink{Answer}}}}$

$x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}$

Step-by-step explanation:

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

We have to find the value of x and y by using cross multiplication method.

$For \ cross \ multiplication \ method \ we \ have\\\\\dfrac{x}{b_1c_2-b_2c_1}=\dfrac{y}{c_1a_2-c_2a_1}=\dfrac{1}{a_1b_2-a_2b_1}\\\\\\5x-3y-2=0 \ and \ 4x+7y+3=0\\\\\\we \ have\\\\a_1=5 \ b_1=-3 \ and \ c_1=-2\\\\\\a_2=4 \ b_2=7 \ and \ c_2=3\\\\\\putting \ value \ in \ formula$

$\dfrac{x}{(-3\times3)-(7\times-2)}=\dfrac{y}{(-2\times4)-(3\times5)}=\dfrac{1}{(5\times7)-(4\times-3)}\\\\\\ \dfrac{x}{-9+14}= \dfrac{1}{35+12} \ and \ \dfrac{y}{-8-15}= \dfrac{1}{35+12}\\\\\\x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}$

So we get our answer  

$x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47}$

$Verification\\\\\\putting \ x=\dfrac{5}{47} \ and \ y=-\dfrac{23}{47} \ in \ 5x-3y=2\\\\\\\L.H.S.=(5\times\dfrac{5}{47})-3\times(-\dfrac{23}{47})\\\\\\L.H.S.=\dfrac{25+69}{47}=2\\\\\\L.H.S.=R.H.S\\\\Now \ putting \ in \ 4x+7y=-3\\\\\\L.H.S.=(4\times\dfrac{5}{47})+(7\times-\dfrac{23}{47})\\\\\\L.H.S.=\dfrac{20-161}{47}\\\\\\L.H.S=\dfrac{-141}{47}=-3\\\\\\L.H.S.=R.H.S\\\\\\Hence \ we \ verified \ it.$