please help

 

A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.  

 

Call the first number X and call the second number Y. 

 

                                                                        X + 2Y  =  14      (eq 1)  

                                                                        2X + Y  =  10      (eq 2)  

 

Multiply both sides of equation 1 by 2              2X + 4Y  =  28    (eq 3)

Subtract equation 2 from equation 3                        3Y  =  18  

Divide both sides by 3                                                 Y  =  6    

 

Substitute 6 for the Y in equation 2                   2X  +  6  =  10    

Subtract 6 from both sides                                        2X  =  4   

Divide both sides by 2                                                 X  =  2    

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