The sum of two numbers is 35 and their difference is 7. What are the two numbers?
x + y = 35
x - y = 7
Can you finish it from this step?
28+7=38
35-28=7
To find the two numbers, we'll set up a system of equations based on the given information.
Let's assume the two numbers are x and y, where x is the larger number.
We can use the following equations:
Equation 1: x + y = 35
Equation 2: x - y = 7
To solve this system of equations, we have a few options. One method is substitution:
Step 1: Solve Equation 2 for x: x = 7 + y
Step 2: Substitute the value of x in Equation 1: 7 + y + y = 35
Step 3: Combine like terms: 2y + 7 = 35
Step 4: Move constants to the other side of the equation: 2y = 35 - 7
Step 5: Simplify: 2y = 28
Step 6: Divide both sides of the equation by 2: y = 28 / 2
Step 7: Solve for y: y = 14
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x:
Using Equation 1: x + 14 = 35
Combine like terms: x = 35 - 14
Simplify: x = 21
Therefore, the two numbers are 21 and 14.