Question

Chapter = Linnear simulation equation. Please answer it fast whose answer is correct I give it brainlieast answer​

Answer 1

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

$\bullet{\mapsto} \: \sf x \: + \: 2y \: = \: 19 \: , \: x \: + \: 3y \: = \: 24.$

$\bullet{\mapsto} \: \sf Find \: x \: and \: y.$

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

$\bullet{\leadsto} \: \sf x \: + \: 2y \: = \: 19 \: \longrightarrow \: \boxed{1}$

$\bullet{\leadsto} \: \sf x \: + \: 3y \: = \: 24 \: \longrightarrow \: \boxed{2}$

$\bullet{\leadsto} \: \sf Taking \: \boxed{1} \: ,$

$\bullet{\leadsto} \: \sf x \: + \: 2y \: = \: 19$

$\bullet{\leadsto} \: \sf x \: = \: 19 \: - \: 2y \: \longrightarrow \: \boxed{3}$

$\bullet{\leadsto} \: \sf Substituting \: \boxed{3} \: i.e \: x \: in \: \boxed{2} \: ,$

$\bullet{\leadsto} \: \sf x \: + \: 3y \: = \: 24$

$\bullet{\leadsto} \: \sf 19 \: - \: 2y \: + \: 3y \: = \: 24$

$\bullet{\leadsto} \: \sf - \: 2y \: + \: 3y \: = \: 24 \: - \: 19$

$\bullet{\leadsto} \: \sf y \: = \: 24 \: - \: 19$

$\bullet{\leadsto} \: \boxed{\sf y \: = \: 5.}$

$\bullet{\leadsto} \: \sf Substituting \: y \: = \: 5 \: in \: \boxed{1} \: ,$

$\bullet{\leadsto} \: \sf x \: + \: 2y \: = \: 19$

$\bullet{\leadsto} \: \sf x \: + \: 2 \: * \: 5 \: = \: 19$

$\bullet{\leadsto} \: \sf x \: + \: 10 \: = \: 19$

$\bullet{\leadsto} \: \sf x \: = \: 19 \: - \: 10$

$\bullet{\leadsto} \: \boxed{\sf x \: = \: 9.}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

$\bullet{\mapsto} \: \boxed{\therefore{\sf x \: = \: 9 \: , \: y \: = \: 5.}}$

$\bullet{\mapsto} \: \boxed{\therefore{\sf (9,5) \: is \: the \: solution \: for \: the \: given \: linear \: equations.}}$

$\huge{\bf{\purple{\mathfrak{Verification:-}}}}$

$\bullet{\leadsto} \: \sf x \: + \: 2y \: = \: 19 \: \longrightarrow \: \boxed{1}$

$\bullet{\leadsto} \: \textsf{Substituting x = 9 and y = 5,}$

$\bullet{\leadsto} \: \sf x \: + \: 2y \: = \: 19$

$\bullet{\leadsto} \: \sf 9 \: + \: 2 \: * \: 5 \: = \: 19$

$\bullet{\leadsto} \: \sf 9 \: + \: 10 \: = \: 19$

$\bullet{\leadsto} \: \sf 19 \: = \: 19$

$\bullet{\leadsto} \: \sf x \: + \: 3y \: = \: 24 \: \longrightarrow \: \boxed{2}$

$\bullet{\leadsto} \: \textsf{Substituting x = 9 and y = 5,}$

$\bullet{\leadsto} \: \sf x \: + \: 3y \: = \: 24$

$\bullet{\leadsto} \: \sf 9 \: + \: 3 \: * \: 5 \: = \: 24$

$\bullet{\leadsto} \: \sf 9 \: + \: 15 \: = \: 24$

$\bullet{\leadsto} \: \sf 24 \: = \: 24$

$\bullet{\leadsto} \: \textsf{Hence, verified.}$

$\huge{\bf{\blue{\mathfrak{Extra \: Information:-}}}}$

$\bullet{\leadsto}$ An equation of the form ax + by + c = 0, where a, b, c are real numbers and at least one of a or b is not zero i.e a² + b² ≠ 0, then it is called a linear equation in two variables x and y.

$\bullet{\leadsto}$ A linear equation in two variables has infinitely many solutions (Here, only 1 linear equation in 2 variables).

Answer 2

$\Large{\textsf{\textbf{\underline{\underline{Given\::}}}}}$

⠀⠀⠀⠀❶ ${\textsf{\textbf{x\:+\:2y\:=\:19\:}}}$

⠀⠀⠀⠀❷ ${\textsf{\textbf{x\:+\:3y\:=\:24\:}}}$

$\Large{\textsf{\textbf{\underline{\underline{To\:do\::}}}}}$

• The value of x & y.

$\Large{\textsf{\textbf{\underline{\underline{Solution\::}}}}}$

$\dashrightarrow\:\tt{\begin{cases} x\:+\:2y\:=\:19 ---(1) \\ \\ x\:+\:3y\:=\:24 ---(2) \end{cases}\:}$

Substracting equation (1) from equation (2), we get

$\dashrightarrow\:\tt{ x\:+\:3y \: -\: \left( x\:+\:2y\right)\:=\:24\:-\:19\:}$

$\dashrightarrow\:\tt{ x\:+\:3y \: -\: x\:-\:2y\:=\:5\:}$

$\dashrightarrow\:\tt{ 3y \:-\:2y\:=\:5\:}$

$\dashrightarrow\:{\textsf{\textbf{\pink{ y\:=\:5\:}}}}$

Putting the value of y in equation (1), we get

$\dashrightarrow\:\tt{ x\:+\:2\times{5}\:=\:19\:}$

$\dashrightarrow\:\tt{ x\:+\:10\:=\:19\:}$

$\dashrightarrow\:\tt{ x\:=\:19\:-\:10\:}$

$\dashrightarrow\:{\textsf{\textbf{\pink{ x\:=\:9\:}}}}$

⠀⠀⠀⠀⠀⠀⠀$\Large{\textsf{\textbf{\underline{\underline{Verification\::}}}}}$

Let's play it,

Putting the resulting values of x & y in the equation (2) as,

$\dashrightarrow\:\tt{ 9\:+\:3\times{5}\:=\:24\:}$

$\dashrightarrow\:\tt{ 9\:+\:15\:=\:24\:}$

$\dashrightarrow\:\tt{ 24\:=\:24\:}$

⠀⠀⠀⠀⠀$\:\red\star\:\:\bf{\underline{\blue{ Hence\: verified\:}}}\:\:\red\star$