How many solutions does the system have? x + 3y = 0 12y = -4x
Understand the Problem
The question asks to determine the number of solutions for the given system of linear equations. We'll need to analyze the relationship between the equations to determine if they represent the same line (infinite solutions), parallel lines (no solutions), or intersecting lines (one solution).
Answer
Infinitely many solutions
Answer for screen readers
Infinitely many solutions
Steps to Solve
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Rewrite the second equation We want to get the second equation in a form similar to the first equation, so we add $4x$ to both sides: $12y = -4x$ $4x + 12y = 0$
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Simplify the second equation Divide the second equation by 4: $(4x + 12y)/4 = 0/4$ $x + 3y = 0$
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Compare the equations Now we have the following system of equations: $x + 3y = 0$ $x + 3y = 0$ Since both equations are identical, they represent the same line.
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Determine the number of solutions When the equations represent the same line, there are infinitely many solutions because every point on the line satisfies both equations.
Infinitely many solutions
More Information
When two linear equations in a system are multiples of each other, they represent the same line. This results in an infinite number of solutions since every point on the line satisfies both equations.
Tips
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