QuestionDetermine the number of solutions of the system. The systom has no solution. The systom has one solution. The system has infinitely many solutions.
Studdy Solution
STEP 1
What is this asking?
We've got two equations, and we need to figure out if they cross paths, never meet, or are the same line!
Watch out!
Don't just assume things!
Make sure you actually solve the system to see what's going on.
STEP 2
1. Set up the system
2. Solve for
3. Solve for
4. Check the solution
STEP 3
Alright, let's **rewrite** our equations nice and neat: This makes it super clear what we're working with!
STEP 4
Since both equations are already solved for , we can **set them equal** to each other:
This is where the magic happens!
We've turned two equations into one!
STEP 5
Now, let's **isolate** that .
First, **add** to both sides:
STEP 6
Next, **subtract** 5 from both sides:
STEP 7
Finally, **divide** both sides by 2: Boom! We found our ** value**: !
STEP 8
Let's plug our shiny new ** value** () back into one of the original equations.
I'm feeling the first one:
STEP 9
Simplify that bad boy: Woohoo! We also found our ** value**: !
STEP 10
Let's double-check our work by plugging *both* ** and ** into the *other* equation (the second one this time):
It works!
High five!
STEP 11
Since we found a single, beautiful solution (, ), the system has *one* solution.
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