SOLUTION: Need help with writing the following problem as a system of two equations in two unknowns. Solve the system using the substitution method: The sum of two numbers is 2, and their

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Need help with writing the following problem as a system of two equations in two unknowns. Solve the system using the substitution method: The sum of two numbers is 2, and their       Log On


   

Question 202069: Need help with writing the following problem as a system of two equations in two unknowns. Solve the system using the substitution method:
The sum of two numbers is 2, and their difference is 26. Find the numbers.
Not even sure where to start..
Here is my try:
x+y=2=26?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, we need to translates the word problems into equations:

"The sum of two numbers is 2" translates to x%2By=2


and "their difference is 26" means that x-y=26


Note: this implies that x%3Ey




So we then get the system of equations:


system%28x%2By=2%2Cx-y=26%29


x%2By=2 Start with the first equation.


y=2-x Subtract x from both sides.


y=-x%2B2 Rearrange the terms.


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x-%28-x%2B2%29=26 Now plug in y=-x%2B2 into the second equation.


x%2Bx-2=26 Distribute.


2x-2=26 Combine like terms on the left side.


2x=26%2B2 Add 2 to both sides.


2x=28 Combine like terms on the right side.


x=%2828%29%2F%282%29 Divide both sides by 2 to isolate x.


x=14 Reduce.


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Since we know that x=14, we can use this to find y.


x%2By=2 Go back to the first equation.


14%2By=2 Plug in x=14.


y=2-14 Subtract 14 from both sides.


y=-12 Combine like terms on the right side.


So the solutions are x=14 and y=-12.


This means that the two numbers are 14 and -12