atlantisbennett
19

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

$\left \{ {{7*x - 3*y=25} \atop {2*x + 5*y=95}} \right.$ $\left \{ {{7x - 3y=25}(I) \atop {2x + 5y=95}(II)} \right.$ $\left \{ {{7x - 3y=25}simplify*(5) \atop {2x + 5y=95}simplify*(3)} \right.$ $\left \{ {{35x - \diagup\!\!\!\! 15 y=125} \atop {6x + \diagup\!\!\!\! 15y=285}} \right.$ $\left \{ {{35x =125} \atop {6x =285}} \right.$ $41x = 410$ $\boxed{x=10}$ Replace the value of "x" in the second equation (II) to find the value of "y", thus: $2x + 5y=95$ $2*(10)+5y = 95$ $20+5y=95$ $5y=95-20$ $5y=75$ $y = \frac{75}{5}$ $\boxed{y=15}$ The numbers (10,15)