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

Write Equations: Write down the system of equations to analyze. The system is: \[ \begin{cases} 20x - 5y = 5 \\ 4x - y = 1 \end{cases} \]Compare Equations: Look for a quick way to compare the two equations. Notice that the second equation can be multiplied by 5 to see if it becomes similar to the first equation. Multiplying the second equation by 5 gives us: \[ 5(4x - y) = 5(1) \] \[ 20x - 5y = 5 \]Identify Same Line: Compare the new form of the second equation with the first equation. After multiplying the second equation by 5, we see that it becomes identical to the first equation: \[ 20x - 5y = 5 \] This means that the two equations are actually the same line.Conclude Solutions: Conclude the number of solutions for the system. Since both equations represent the same line, the system does not have a unique solution. Instead, it has infinitely many solutions because every point on the line is a solution to the system.

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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

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

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Math Problems

Algebra 2

Find the number of solutions to a system of equations

Full solution

Q. 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

Write Equations: Write down the system of equations to analyze. $\newline$ The system is: $\newline$ $\begin{cases} 20x - 5y = 5 \\ 4x - y = 1 \end{cases}$
Compare Equations: Look for a quick way to compare the two equations. Notice that the second equation can be multiplied by $5$ to see if it becomes similar to the first equation. $\newline$ Multiplying the second equation by $5$ gives us: $\newline$ $5(4x - y) = 5(1)$ $\newline$ $20x - 5y = 5$
Identify Same Line: Compare the new form of the second equation with the first equation. $\newline$ After multiplying the second equation by $5$ , we see that it becomes identical to the first equation: $\newline$ $20x - 5y = 5$ $\newline$ This means that the two equations are actually the same line.
Conclude Solutions: Conclude the number of solutions for the system. $\newline$ Since both equations represent the same line, the system does not have a unique solution. Instead, it has infinitely many solutions because every point on the line is a solution to the system.