[tex]\bold{\rm{Given}}\text{ : If y - 3x = 9, 7x + y = 25, what is the value of x and y}?[/tex]
[tex]\bold{\rm{Solution}} \text{: We'll solve this by substitution method}[/tex]
[tex] \dashrightarrow y - 3x = 9 \\ \\ \dashrightarrow \boxed{y = 9 + 3x } \qquad .. \sf eq(1)[/tex]
[tex]\text{we got the value of y now getting the value of x}[/tex]
[tex] \looparrowright 7x + y = 25 \\ \\ \looparrowright 7x = 25 - y \\ \\ \looparrowright \boxed{x = \frac{25 - y}{7}} \qquad .. \sf eq(2)[/tex]
[tex]\text{Now, putting y = 9 + 3x in eq(2)}[/tex]
[tex] \hookrightarrow x = \frac{25 - y}{7} \\ \\ \hookrightarrow x = \frac{25 - 9 + 3x}{7} \\ \\ \hookrightarrow 7x = 25 - 9 + 3x \\ \\ \hookrightarrow 7x - 3x = 16 \\ \\ \hookrightarrow 4x = 16 \\ \\ \hookrightarrow x = \frac{16}{4} \\ \\ \star \quad \boxed{ \green{ \frak{ x = 4}}}[/tex]
[tex]\text{Now we know the value of x, for getting y we need to put x in eq(1)}[/tex]
[tex] : \implies y = 9 + 3x \\ \\ : \implies y = 9 + 3(4) \\ \\ : \implies y = 9 + 12 \\ \\ \star \quad \boxed{\frak{ \green{y = 21}}}[/tex]
[tex] \text{Hence, values of x and y are} \: \frak{ \green{4}} \: \text{and} \: \frak{ \green{21}} \: \text{respectively}.[/tex]
