Answer/Step-by-step explanation:
Given:
[tex] \frac{4}{x} - \frac{3}{y} = 1 [/tex] ---› Equation 1
[tex] \frac{8}{x} + \frac{9}{y} = 7 [/tex] ---› Equation 2
Solution:
✔️Equation 1 × 3:
[tex] \frac{4}{x}*3 + \frac{3}{y}*3 = 1*3 [/tex]
[tex] \frac{12}{x} + \frac{9}{y} = 3 [/tex] ---› Equation 3.
✔️Equation 2 + Equation 3:
[tex] \frac{8}{x} + \frac{9}{y} = 7 [/tex] ---› Equation 2
[tex] \frac{12}{x} + \frac{9}{y} = 3 [/tex] ---› Equation 3.
Thus:
[tex] \frac{-4}{x} = 10 [/tex]
Cross multiply
[tex] 10x = -4 [/tex]
Divide both sides by 10
[tex] x = -\frac{4}{10} [/tex]
[tex] x = -\frac{2}{5} [/tex]
✔️Find y:
Substitute x = -2/5 into equation 1
[tex] \frac{4}{x} - \frac{3}{y} = 1 [/tex] ---› Equation 1
[tex] \frac{4}{\frac{-2}{5}} - \frac{3}{y} = 1 [/tex]
[tex] \frac{4}*{\frac{5}{-2}} - \frac{3}{y} = 1 [/tex]
[tex] -10 - \frac{3}{y} = 1 [/tex]
Add 10 to both sides
[tex] - \frac{3}{y} = 1 + 10 [/tex]
[tex] \frac{-3}{y} = 11 [/tex]
Cross multiply
[tex] 11y = -3 [/tex]
Divide both sides by 11
[tex] y = -\frac{3}{11} [/tex]
