Types of Solutions for a System

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

Question

Types of Solutions for a System

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

BlackTom AI · Accepted Answer

Here are the equations: 2x + y = 4 and 8x + 4y = 20.
Consider scaling the first equation by 4: 4*(2x + y) = 4*4, which gives 8x + 4y = 16.
Now compare this scaled equation to the second equation, which is 8x + 4y = 20.
They have the same left-hand side but different right-hand sides (16 vs 20), which means the two equations cannot be satisfied simultaneously.
Geometrically, the two lines represented by these equations are parallel: both have the same slope but different intercepts, so they never intersect.
As a result, there is no pair (x, y) that satisfies both equations at the same time.

MAT-265-OD24-02-7799

Types of Solutions for a System Solve the given system of equations. Choose the best answer.

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