Question

the difference between seven times one number and three times a second number is 25. The sum of twice the first and five times the second is 95, Find the numbers

Answer 1

`\left \{ {{7*x - 3*y=25} \atop {2*x + 5*y=95}} \right.`


`\left \{ {{7x - 3y=25}(I) \atop {2x + 5y=95}(II)} \right.`


`\left \{ {{7x - 3y=25}simplify*(5) \atop {2x + 5y=95}simplify*(3)} \right.`


`\left \{ {{35x - \diagup\!\!\!\! 15 y=125} \atop {6x + \diagup\!\!\!\! 15y=285}} \right.`


`\left \{ {{35x =125} \atop {6x =285}} \right.`


`41x = 410`


`\boxed{x=10}`

Replace the value of "x" in the second equation (II) to find the value of "y", thus:

`2x + 5y=95`

`2*(10)+5y = 95`

`20+5y=95`

`5y=95-20`

`5y=75`

`y = (75)/(5)`

`\boxed{y=15}`


The numbers (10,15)