Translate to a system of equations and solve using the addition method.
The sum of two numbers is88. The difference is 22.Find the numbers?
My answer:
I started but i think that i am wrong.
x + y = 88
y = -x +88
y = -1x + 88
now once i substituted
x -1x + 88 = 88
see i don't know if i am doing this correctly.
You wrote only one equation and you need two.
x+y=88 is ok
The second equation is
x-y=22.Also note that the problem asks for a solution by addition, not by substitution.
solve for x and y.
so then that means that the solution is (55,33)
yes
To understand how to solve the system of equations using the addition method, let's break it down step by step.
1. Define the variables: Let x represent one of the numbers, and let y represent the other number.
2. Write the equations: We are given two pieces of information. The first states that the sum of the two numbers is 88:
x + y = 88
The second piece of information states that the difference between the two numbers is 22:
x - y = 22
These two equations form a system that we need to solve simultaneously.
3. Solve the system using the addition method: In this method, we aim to eliminate one of the variables by adding the two equations together. This will result in a new equation with only one variable.
To eliminate the y variable, we can add the two equations together:
(x + y) + (x - y) = 88 + 22
Simplify the equation:
x + y + x - y = 110
Combine like terms:
2x = 110
4. Solve for x: Divide both sides of the equation by 2 to isolate the x variable:
2x/2 = 110/2
x = 55
5. Find y: Substitute the value of x back into one of the original equations. Let's use the first equation:
x + y = 88
55 + y = 88
Subtract 55 from both sides:
y = 88 - 55
y = 33
6. Verify the solution: Check if the values of x and y satisfy both equations:
55 + 33 = 88 (sum equation)
55 - 33 = 22 (difference equation)
Since both equations are satisfied, the solution is correct.
Therefore, the numbers are x = 55 and y = 33.