Question

solve the equation 5x-3y =1 2x +5y=19​

Answer 1

Answer:

Step-by-step explanation:

5x-3y = 1

5x = 1 + 3y

x = 1+3y / 5

2x+5y=19

2x=19-5y

x=19-5y / 2

1+3y / 5 = 19-5y /2

2(1+3y) = 5(19-5y)    ( by cross multiplying)

2+6y = 95-25y

6y+25y = 95-2

31y=93

y = 93/31

y=3

Answer 2

Given,

$\large \rm{}5x-3y =1 \: \: \: \: \cdots(i) \\ \large \rm{} 2x +5y=19\: \: \: \: \cdots(ii)$

Multiplying Equation (i) & Equation (ii) with 2 and 5 respectively, we get,

$\large \rm{}10x - 6y = 2 \: \: \: \: \cdots(iii) \\ \large\rm 10x + 25y = 95\: \: \: \: \cdots(iv)$

Subtracting Equation (iii) from Equation (iv), we get,

$\to \tt{}10x + 25y - (10x - 6y) = 95 - 2 \\ \to \tt{} \cancel{10x} +2 5y - \cancel{10x} + 6y = 93 \\ \to \tt{}(25 + 6)y = 93 \\ \to \tt{}31y = 93 \\ \\ \to \tt{} \frac{\cancel{31}y}{ \cancel{31}} = \frac{93}{31} \\ \\ \to \tt{}y = \frac{93}{31} \\ \\ \to \tt{}y = \sf\red{3}$

Now, Putting the value of y in equation (i), we get,

$\bf{}x = \frac{1 + 3y}{5} \\ \\ \bf x = \frac{1 + 3(3)}{5} = \frac{1 + 9}{5} \\ \\ \bf{}x = \frac{10}{5} \: \: = \sf \red2$

Thus,

Value of x = 2

Value of y = 3