the sum of two numbers is 60. their difference is 6.
construct a system of equations and algebraically find the value of the smaller number.
aa tysmm
also vivian is such a pretty name but its rare too
a + b = 60
a - b = 6
adding equations ... 2 a = 66 (b's cancel)
solve for a , then find b
Vivian's technique works
... but only in a case like this
x + y = 60
x - y = 6
x = 60 - y
60 - y - y = 6
-2y = -54
y = 27
x + 27 = 60
x = 33
To construct a system of equations, let's first assign variables to the two unknown numbers. Let's call the larger number "x" and the smaller number "y".
According to the given information:
1. The sum of the two numbers is 60, so we can write the equation:
x + y = 60
2. The difference between the two numbers is 6, so we can write the equation:
x - y = 6
Now, we have a system of two equations:
Equation 1: x + y = 60
Equation 2: x - y = 6
To algebraically find the value of the smaller number, we can solve the system of equations. One method is the elimination method:
1. Add the two equations together to eliminate the variable "y":
(x + y) + (x - y) = 60 + 6
2x = 66
2. Divide both sides of the equation by 2 to isolate "x":
x = 66 / 2
x = 33
3. Substitute the value of x (33) back into either of the original equations. Let's use Equation 1:
33 + y = 60
4. Solve for y by subtracting 33 from both sides:
y = 60 - 33
y = 27
Therefore, the smaller number is 27.
So, the algebraic solution shows that the value of the smaller number is 27.