How many solutions does the system have? {[20 x-5y=5],[4x-y=1]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Question

How many solutions does the system have?  {[20 x-5y=5],[4x-y=1]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Bytelearn · Accepted Answer

Write System of Equations: Write down the system of equations to analyze. The system is: $$ \begin{cases}  20x - 5y = 5 \ 4x - y = 1  \end{cases} $$ We want to determine if this system has exactly one solution, no solutions, or infinitely many solutions.Simplify the System: Look for a way to simplify the system. Notice that the first equation can be simplified by dividing every term by 5, which would give us the second equation. Let's do that: $$ \frac{20x}{5} - \frac{5y}{5} = \frac{5}{5} $$ $$ 4x - y = 1 $$ This is the same as the second equation in the system.Determine Relationship: Determine the relationship between the two equations. Since the simplified form of the first equation is identical to the second equation, we have two identical equations. This means that every solution to one equation is also a solution to the other.Conclude Number of Solutions: Conclude the number of solutions. Because the two equations are identical, the system does not have a unique solution. Instead, it has infinitely many solutions, as every point on the line represented by the equation $ 4x - y = 1 $ is a solution to the system.

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 20 x-5 y=5 \\ 4 x-y=1 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

Full solution

More problems from Write an equation word problem

Related topics

How many solutions does the system have?\newline{20x−5y=54x−y=1 \left\{\begin{array}{l} 20 x-5 y=5 \\ 4 x-y=1 \end{array}\right. {20x−5y=54x−y=1​\newlineChoose 111 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 20 x-5 y=5 \\ 4 x-y=1 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions