Answer: [tex](25,9)[/tex]
Step-by-step explanation:
In order to write an equivalent equation for the first equation, you can multiply both sides by 15:
[tex](15)(\frac{x}{5}+\frac{y}{3})=(8)(15)\\\\3x+5y=120[/tex]
Then, you get this system of equations:
[tex]\left \{ {{3x+5y=120} \atop {x-2y=7}} \right.[/tex]
Now, you can apply the Elimination Method to solve the system of equations:
1. Multiply the second equation byb -3.
2. Add the equations.
3. Solve for "y".
Then:
[tex]\left \{ {{3x+5y=120} \atop {-3x+6y=-21}} \right.\\.....................\\11y=99\\\\y=9[/tex]
4. Substitute the value of "y" into any original equation and solve for "x" in order to find its value:
[tex]x-2(9)=7\\\\x=7+18\\\\x=25[/tex]
5. The solution is:
[tex](25,9)[/tex]
