Answer:
1) The system of equations is [tex]5x+4y=75[/tex] and [tex]x+y=18[/tex]
2) The first number is [tex]3[/tex] and the second number is [tex]15[/tex]
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: [tex]=[/tex]
Then, the sum of 5 times "x" and 4 times "y" is 75, can written as:
[tex]5x+4y=75[/tex]
And "The sum of the two numbers is 18" can written as:
[tex]x+y=18[/tex]
Therefore, the System of equations is:
[tex]\left \{ {{5x+4y=75} \atop {x+y=18}} \right.[/tex]
2) You can use the Elimination Method to solve it:
- Multiply the second equation by -5, add the equations and then solve for "y":
[tex]\left \{ {{5x+4y=75} \atop {-5x-5y=-90}} \right.\\......................\\-y=-15\\\\y=15[/tex]
- Substitute the value of "y" into any original equation and solve for "x":
[tex]x+15=18\\\\x=18-15\\\\x=3[/tex]
