Question
Ask by Evans Mcguire. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The system has infinitely many solutions.
Solution
Solve the system of equations
Solve the system of equations by following steps:
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
- step1: Substitute the value of
- step2: Simplify:
- step3: Calculate:
- step4: Alternative Form:
The system of equations has infinitely many solutions. This means that the lines represented by the equations intersect at every point on the line, and there are no specific coordinates that satisfy both equations. Therefore, the system is consistent and has infinitely many solutions.
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Simplify this solution Beyond the Answer
To solve the system of equations by graphing, we first rewrite each equation in slope-intercept form (y = mx + b).
-
The first equation:
- Rearranging it gives:
- Dividing all terms by 2, we get:
- Rearranging it gives:
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The second equation is already simplified:
Now we see that both equations are identical, meaning they represent the same line. Thus, there are infinitely many solutions along this line.
To express this mathematically, we can choose any
However, since the two equations represent the same line, we conclude that the system has infinitely many solutions.
Final answer: Infinitely many solutions (e.g.,
