5. Write a system of equations where the sum of two numbers is 10 and the difference is 6. Can you determine the solution without graphing? Guess and check.
Let's call the two numbers x and y.
The first equation states that the sum of the two numbers is 10:
x + y = 10
The second equation states that the difference between the two numbers is 6:
x - y = 6
To solve this system of equations without graphing, we can use the method of substitution or elimination.
Using the substitution method, we can solve the second equation for x:
x = y + 6
Now we can substitute this expression for x in the first equation:
(y + 6) + y = 10
Simplifying:
2y + 6 = 10
Subtracting 6 from both sides:
2y = 4
Dividing both sides by 2:
y = 2
Now we can substitute this value for y back into the second equation to find x:
x - 2 = 6
Adding 2 to both sides:
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 2.
To write a system of equations based on the given conditions, we can use variables to represent the two numbers. Let's call the first number "x" and the second number "y".
From the given information, we have two conditions:
1. The sum of the two numbers is 10: x + y = 10
2. The difference between the two numbers is 6: x - y = 6
Now, to determine the solution without graphing, we can use the method of "guess and check" or substitution.
Let's solve the system using the method of substitution to determine the values of x and y.
From equation (2), we can rewrite it as x = y + 6.
Substituting this value of x into equation (1), we get:
(y + 6) + y = 10
Simplifying this equation, we have:
2y + 6 = 10
Next, we isolate the variable term, 2y, by subtracting 6 from both sides:
2y = 10 - 6
2y = 4
Finally, dividing both sides by 2, we find:
y = 2
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x.
Using equation (2), we have:
x - 2 = 6
Adding 2 to both sides gives us:
x = 8
So, the solution to the system of equations is x = 8 and y = 2.
Hence, without graphing, we were able to determine the solution using the method of "guess and check" or substitution.
To write a system of equations where the sum of two numbers is 10 and the difference is 6, we can assign variables to each of the numbers.
Let's call the first number x, and the second number y.
From the given information, we can set up two equations:
1) The sum of the two numbers is 10:
x + y = 10
2) The difference of the two numbers is 6:
x - y = 6
Now, we have a system of equations:
x + y = 10
x - y = 6
To determine the solution without graphing, we can use the method of guessing and checking. We can start by making a guess for one of the variables and then solve for the other variable.
Let's assume a value for x, and see if we can find a corresponding value for y:
Assuming x = 8
Substituting x = 8 into equation (1):
8 + y = 10
y = 10 - 8
y = 2
Checking if this satisfies equation (2):
8 - 2 = 6
6 = 6
As both equations are satisfied, the numbers x = 8 and y = 2 are a possible solution to the system of equations.
Therefore, the solution to the system of equations x + y = 10 and x - y = 6 is x = 8 and y = 2.