Dorothy is thinking of two numbers. The sum of the numbers is 40 and the difference is 6. write a system of equations and use elimination method to find the two numbers.
x + y = 40
x - y = 6
Add the two equations and solve for x. Insert that value into one of the equations to find y.
y=46
To solve this problem using the elimination method, we need to set up a system of equations based on the given information.
Let's call the first number x and the second number y.
From the problem statement, we know two things:
1. The sum of the numbers is 40: x + y = 40.
2. The difference between the numbers is 6: x - y = 6.
Now, we have a system of two equations:
Equation 1: x + y = 40
Equation 2: x - y = 6
To solve this system using the elimination method, we'll eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable x by adding the two equations:
Equation 1 + Equation 2: (x + y) + (x - y) = 40 + 6
This simplifies to: 2x = 46
Now, to isolate x, we divide both sides of the equation by 2:
2x / 2 = 46 / 2
x = 23
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use Equation 1:
23 + y = 40
Subtracting 23 from both sides gives us:
y = 40 - 23
y = 17
Therefore, the two numbers that Dorothy is thinking of are 23 and 17.
x=23
y=46