Question

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

Answer 1

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! :)