Question

Solve 2x + 3y = 19

x – 3y = 5​

Answer 1

${\large{\underline{\red{\text{Answer :-}}}}}$

2x + 3y = 19 --- (1)

x – 3y = 5 ----(2)

We add both equation

$\dashrightarrow\sf{2x + 3y + (x - 3y) = 19 + 5} \\ \\ \dashrightarrow\sf{2x + x + 3y - 3y = 24} \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{3x = 24} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{x = \frac{24}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{ \boxed{ \sf x =8 }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substitute x = 8 in equation (1)

$\dashrightarrow\sf{2(8) + 3y = 19} \\ \\ \dashrightarrow\sf{16 + 3y = 19} \: \: \: \\ \\ \dashrightarrow\sf{3y = 19 - 16} \: \: \\ \\ \dashrightarrow\sf{3y = 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{y = \frac{3}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{ \boxed{ \sf y = 1}} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Verification

putting x = 8 and y = 1

$\dashrightarrow\sf{2(8) + 3(1) = 19} \\ \\ \dashrightarrow\sf{16 + 3 = 19} \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow\sf{19 = 19} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence Verified

_________________________________