Find two numbers
a
and
b
whose sum
a
+
b
is 2 and whose difference
a
−
b
is -4?
To find two numbers, a and b, whose sum is 2 and whose difference is -4, we can set up a system of equations and solve for a and b.
Let's start by assigning variables to the unknown numbers:
a = the first number
b = the second number
Since the sum of a and b is 2, we can write the equation:
a + b = 2 ------ Equation 1
And since the difference of a and b is -4, we can write the equation:
a - b = -4 ------ Equation 2
Now, we have a system of equations with two variables (a and b). To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution to solve the system:
1. From Equation 2, let's isolate 'a' to solve for it:
a = b - 4
2. Now, substitute the value of 'a' into Equation 1:
(b - 4) + b = 2
3. Simplify and solve for 'b':
2b - 4 = 2
2b = 6
b = 3
4. Substitute the value of 'b' back into Equation 2 to solve for 'a':
a - 3 = -4
a = -4 + 3
a = -1
So, the two numbers that satisfy the given conditions are:
a = -1
b = 3
a+b = 2
a-b = -4
add the two lines and you get
2a = -2
and the rest is easy.