Set up a linear system and solve. The sum of two integers is 29. The larger is 10 less than twice the smaller. Find the two integers.

Question

Set up a linear system and solve.

The sum of two integers is 29. The larger is 10 less than twice the smaller. Find the two integers.

Answer 1

two integers must be assigned two distinct variables

first integer: a

second integer: b

a + b = 29 sum is 29

2a - 10 = b larger is 10 less than twice the smaller

by substituting the second equation into the first

a + (2a - 10) = 29

3a -10 = 29 combine like terms

3a = 39 add 10 on both sides

a = 13 divide 3 on both sides

using a +b = 29

13 +b = 29

b = 16

So the two integers are 13 and 16.