Mathematics
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

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Travelstead238

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

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