The sum of the two numbers is 42. The smaller number is 63 less than twice the larger number. Find both numbers.



STEP 1: identify variables and equations x= larger number y= smaller number FIRST EQUATION x + y= 42 SECOND EQUATION y= 2x - 63 STEP 2: substitute the y value in second equation in for y in first equation x + y= 42 substitute y value from 2nd equation x + (2x - 63)= 42 combine like terms 3x - 63= 42 add 63 to both sides 3x= 105 divide both sides by 3 x= 35 larger number STEP 3: find y value; substitute step 2 x value into either original equation x + y= 42 35 + y= 42 subtract 35 from both sides y= 7 smaller number ANSWER: larger number is x= 35; smaller number is y= 7. Hope this helps! :)

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