Answer:
1) The system of equations is
and ![x+y=18](https://tex.z-dn.net/?f=x%2By%3D18)
2) The first number is
and the second number is ![15](https://tex.z-dn.net/?f=15)
Step-by-step explanation:
1) Let be "x" the first number and "y" the second number.
Remember that:
a- The word "times" indicates multiplication.
b- A sum is the result of an addition.
c- "Is" indicates this sign: ![=](https://tex.z-dn.net/?f=%3D)
Then, the sum of 5 times "x" and 4 times "y" is 75, can written as:
![5x+4y=75](https://tex.z-dn.net/?f=5x%2B4y%3D75)
And "The sum of the two numbers is 18" can written as:
![x+y=18](https://tex.z-dn.net/?f=x%2By%3D18)
Therefore, the System of equations is:
![\left \{ {{5x+4y=75} \atop {x+y=18}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B5x%2B4y%3D75%7D%20%5Catop%20%7Bx%2By%3D18%7D%7D%20%5Cright.)
2) You can use the Elimination Method to solve it:
- Multiply the second equation by -5, add the equations and then solve for "y":
![\left \{ {{5x+4y=75} \atop {-5x-5y=-90}} \right.\\......................\\-y=-15\\\\y=15](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B5x%2B4y%3D75%7D%20%5Catop%20%7B-5x-5y%3D-90%7D%7D%20%5Cright.%5C%5C......................%5C%5C-y%3D-15%5C%5C%5C%5Cy%3D15)
- Substitute the value of "y" into any original equation and solve for "x":
![x+15=18\\\\x=18-15\\\\x=3](https://tex.z-dn.net/?f=x%2B15%3D18%5C%5C%5C%5Cx%3D18-15%5C%5C%5C%5Cx%3D3)