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
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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) (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
and "their difference is 26" means that
Note: this implies that
So we then get the system of equations:
Start with the first equation.
Subtract from both sides.
Rearrange the terms.
-------------------------------------------
Now plug in into the second equation.
Distribute.
Combine like terms on the left side.
Add to both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
-------------------------------------------
Since we know that , we can use this to find .
Go back to the first equation.
Plug in .
Subtract from both sides.
Combine like terms on the right side.
So the solutions are and .
This means that the two numbers are 14 and -12
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