Question

Please help me to solve​

Answer 1

Answer :

• x = 1 and y = -2

Question :

solve the system of linear equations by cross multiplication method

$\sf\longrightarrow3x +7y +17 = 0 \\\sf</p><p>\longrightarrow4x + 5y + 14 = 0$

Step-by-step explanation:

given that :

• 3x + 7y + 17 = 0
• 4x + 5y + 14 = 0

To Find :

• the value of x and y

Solution :

consider the given set of equation

$\qquad\longrightarrow \sf \: 2x + 3y + 8 = 0\\\\\qquad \: \longrightarrow \sf \: 4x + 5y + 14 = 0$

Let us consider the general set of equation :

$\qquad \red\longrightarrow \green{\sf a_1 x+ b_1y+ c_1 =0} \\ \\ \\ \qquad \red\longrightarrow \green{\sf a_2 x+ b_2y+ c_2 =0}$

By cross multiplication we get ,

$\red\longrightarrow \sf \qquad \dfrac{x}{b_1c_2 - b_2c_1} \: \: \: = \: \: \: \dfrac{y}{b_2c_1 - a_1c_1} \: \: \: = \dfrac{1}{a_1b_2 - a_2b_1}$

here ,

$\red\longrightarrow a_1=2 \: \: \: \& \: \: \: a_2=4 \\ \\ \red\longrightarrow b_1 =3 \: \: \& \: \: \: b_2=-5 \\ \\ \red\longrightarrow c_1 =8 \: \: \& \: \: c_2=14$

☆putting value in formula

$\qquad\red\longrightarrow \: \tt \: \: \dfrac{x}{3 \times 14 + 5 \times 8} \: \: \: = \: \: \: \dfrac{y}{4 \times 8 - 2 \times 14} \: \: \: = \: \: \: \dfrac{1}{2 \times (5) - 4 \times 3} \\ \\ \\ \\ \red\longrightarrow \: \tt \: \: \frac{x}{42 - 40} \: \: \: = \: \: \: \frac{y}{32 - 28} \: \: \: = \: \: \: \frac{1}{10 - 12} \\ \\ \\ \\ \red\longrightarrow \tt \: \: \: \frac{x}{2} \: \: \: = \: \: \: \frac{y}{4} \: \: \: = \: \: \: \frac{1}{ - 2} \\ \\ \\ { \boxed{\red\longrightarrow \blue{\underline{ \overline{\green{ \boxed{ \frak{x = 1 \: \: \: \: \: and \: \: \: \: \: \: y = - 2}}}}}}}}$

hence, the value of x = 1 and the value of y = -2