Write two equations that have your two integers as solutions. Show how you built the equations using your integers, numbers used 5 and 8.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.
To build the equations, let's use the integers 5 and 8.
Equation 1:
Let's say our first number is x.
Since our first integer is 5, our equation can be x = 5.
Equation 2:
Let's consider our second number as y.
Since our second integer is 8, our equation can be y = 8.
Now, let's solve the system of equations using the addition/subtraction method. The 5 steps involved are:
Step 1: Add or subtract the two equations to eliminate one variable. Let's add Equation 1 and Equation 2:
(x) + (y) = (5) + (8)
Step 2: Simplify the equation:
x + y = 13
Step 3: Choose one equation to isolate a variable. Let's choose Equation 1:
x = 5
Step 4: Substitute the isolated variable (x = 5) into the other equation (x + y = 13):
5 + y = 13
Step 5: Solve for the remaining variable:
y = 13 - 5
y = 8
Therefore, our solutions are x = 5 and y = 8.
To create two equations with the integers 5 and 8 as solutions, I can use the following steps:
Step 1: Choose a common variable to represent the unknowns in both equations. Let's use the variable 'x'.
Step 2: For the first equation, let's say the sum of our integers is 13. So, the equation can be:
x + x = 13
or simply: 2x = 13
Step 3: For the second equation, let's say the product of our integers is 40. So, the equation can be:
x * x = 40
or simply: x^2 = 40
Now, let's solve this system of equations using the addition/subtraction method:
Step 1: Rewrite the first equation: 2x = 13 as x = 13/2 or x = 6.5
Step 2: Substitute the value of x in either of the original equations. Let's use the first equation, x + x = 13:
6.5 + x = 13
Step 3: Simplify the equation:
7.5 + x = 13
Step 4: Move the constant term to the other side of the equation:
x = 13 - 7.5
Step 5: Therefore, the value of x is:
x = 5.5
So, the solution to the system of equations is x = 5.5.