Answer:
17 is a factor of (8x+19y)
Step-by-step explanation:
Given, 17 is a factor of (3x+5y)
Then,
3x+5y = 17r [where r is an integer]
⇔5y=17r-3x
[tex]\Leftrightarrow y= \frac{17r -3x}{5}[/tex]
∴8x+19y
[tex]=8x+\frac{19({17r -3x})}{5}}[/tex]
[tex]=\frac{40x+323r-57x}{5}[/tex]
[tex]=\frac{323r-17x}{5}[/tex]
[tex]=\frac{17(19r-x)}{5}[/tex]
[tex]=17 \times\frac{19r-x}{5}[/tex]
Which shows that 17 is a factor of (8x+19y)
