Find two numbers whose sum is -64, if twice the first is 1 more than the second

first one --- x

second one -- y
x+y = -64 ---> y = -x-64

2x = y+1
sub the first into that:
2x = -x-64 + 1
3x = -63
x = -21
y = -(-21) - 64 = -43

the two numbers are -21 and -43

check:
yes , their sum is -64
twice the first = -42
one more than the second = -43+1 = -42
All is good!

Let's call the first number x and the second number y.

According to the given information, we can create two equations:

Equation 1: x + y = -64 (Sum of the two numbers is -64)
Equation 2: 2x = y + 1 (Twice the first number is 1 more than the second number)

We can solve this system of equations to find the values of x and y.

From Equation 1, we can isolate x by subtracting y from both sides:
x = -64 - y

Now, substitute this value of x into Equation 2:
2(-64 - y) = y + 1

Simplify the equation:
-128 - 2y = y + 1

Add 2y to both sides:
-128 = 3y + 1

Subtract 1 from both sides:
-129 = 3y

Divide both sides by 3:
y ≈ -43

Substitute the value of y back into Equation 1:
x + (-43) = -64

Add 43 to both sides:
x = -64 + 43

Simplify:
x = -21

Therefore, the two numbers are -21 and -43, with their sum being -64.

To solve this problem, you can use a system of equations. Let's assume the first number is x and the second number is y.

According to the problem statement, the sum of the two numbers is -64, so we can write the equation:
x + y = -64

It is also given that twice the first number is 1 more than the second, which can be written as:
2x = y + 1

Now we have a system of two equations. To find the values of x and y, we can use substitution or elimination method.

Let's use the substitution method:

First, solve the second equation for y in terms of x:
y = 2x - 1

Substitute this value of y in the first equation:
x + (2x - 1) = -64
3x - 1 = -64
3x = -63
x = -63/3
x = -21

Now substitute the value of x back into one of the original equations to find y:
y = 2(-21) - 1
y = -42 - 1
y = -43

So, the two numbers are -21 and -43, with a sum of -64 and twice the first being 1 more than the second.