Find two consecutive integers whose sum is -31

Answer 1

this problem is asking for the values of two unknowns

THINK: System of Equations

You need to come up with as many equations as there are unknowns, in this case 2

Let's call them x, and y

STEP 1: find one way to relate two numbers that add to -31

x + y = -31

STEP 2: find a second way to relate two consecutive numbers

x - y = 1

( for example: two consecutive numbers 9 and 10, 10 - 9 = 1)

STEP 3: pick one of the three methods to solve the system of equations: graph, substitution, and elimination

Let's go with substitution

STEP 4: do it

_

x - y = 1

x + y = -31

_

x = 1 + y <-- come back to this 'x equals' line later

x + y = -31

_

(1 + y) + y = -31 <-- make substitution for x in terms of y

1 + 2y = -31

2y = -31 - 1

2y = -32

y = -32/2

y = -16

Therefore, for x = 1 + y

x = 1 + (-16) <-- make substitution for y, solve for x

x = -15

STEP 5: CHECK

-16 and -15 are consecutive numbers √

-16 + -15 = -31 √

ANSWER:

Two consecutive numbers, whose sum is -31 are -16 and -15

Answer 2

n + (n+1) = -31 --> 2n+1 =-31 --> 2n=-32 --> n=-16 and n+1 =-15