Types of Solutions for a System

Solve the given system of equations. Choose the best answer.

{2x+y=4
8x+4y=20

Question

Types of Solutions for a System

Solve the given system of equations. Choose the best answer.

{2x+y=4
8x+4y=20

BlackTom AI · Accepted Answer

The task presents a pair of linear equations to assess the type of solution. 
First, observe the two equations: 2x + y = 4 and 8x + 4y = 20. 
Next, compare the second equation to a multiple of the first: multiplying the first equation by 4 would yield 8x + 4y = 16, not 20. 
This discrepancy means the two equations do not represent the same line; they are inconsistent with each other.
If the second equation were exactly 4 times the first, the two would be dependent and the system would have infinitely many solutions. However, since 8x + 4y = 20 is not the same as 8x + 4y = 16, the lines are parallel but distinct, leading to no common solution.
Additionally, note that the provided answer options are empty in this prompt, so there is no listed choice to select. In general, when a system yields a contradiction like this, the standard conclusion is that there is no solution. 
Be mindful that, in some contexts, a multiple-equation check helps quickly verify consistency: if one equation is a scalar multiple of the other with a different constant term, no solution exists. Here, the mismatch in the constants reveals the inconsistency.

MAT-265-OD24-02-7799

Types of Solutions for a System Solve the given system of equations. Choose the best answer. {2x+y=4 8x+4y=20

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