Question

Solve the following pair of linear equations x and y by the substitution method 7x - 15y =2 ; x + 2y = 3​

Answer 1

Answer:

x = 49/29 and y = 19/29

Step-by-step explanation:

Given,

7x - 15y = 2     ...(1)

x +  2y = 3     ...(2)

From (1),

7x - 15y = 2

7x = 2 = 15y

x = 2+15y/7

Substitue value of x in (2), we get,

x+2y = 3

(2+15y/7) + 2y = 3

Multiplying both sides by 7, we get,

7 * (2+15y/7) + 7 * 2y = 7 * 3

(2+15y) + 14y = 21

15y + 14y = 21-2

29y = 19

y = 19/29.

Substituing vaule of y in (2), we get,

x + 2y = 3

x + 2 (19/29) = 3

x + (38+29) = 3

x = 3 - 38 / 29

x = ( 3(29) - 38 ) / 29

x = 97-38/29

x = 49/29

Therefore x = 49/29 and y = 19/29

Answer 2

Answer:

$7x - 15y = 2 \\ \: \implies7x = 2 + 15y \\ \implies \: x = \frac{2 + 15y}{7} \: \: \: \: \: \rightarrow(i) \\ \\ x + 2y = 3 \\ \implies\frac{2 + 15y}{7} + 2y = 3 \: (putting \: x = \frac{2 + 15y}{7} ) \\ \implies \frac{2 + 15y + 14y}{7} = 3 \\ \implies15y + 14y = 3 \times 7 - 2 \\ \implies29y = 21 - 2 \\ \implies \: y = \frac{19}{29} \\ \\ \\ \: \: substituting \: the \: value \: of \: y \: in \: equation \: (i) \\ 7x - 15 \times \frac{19}{29} = 2 \\ \implies7x - \frac{285}{29} = 2 \\ \implies7x = 2 + \frac{285}{29} \\ \implies7x = \frac{58 + 285}{29} \\ \\ \: \implies7x = \frac{343}{29 } \\ \\ \implies \: x = \frac{343}{203} \\ \\ \implies \: x = \frac{49}{29} \\ \\ \therefore \: x = \frac{49}{29} \\ \\ y = \frac{19}{29}$