How many solutions does the system have? {[8x+2y=14],[8x+2y=4]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

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How many solutions does the system have?  {[8x+2y=14],[8x+2y=4]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Bytelearn · Accepted Answer

Analyze the system of equations: Let's analyze the system of equations: $$ \begin{cases}  8x + 2y = 14 \ 8x + 2y = 4  \end{cases} $$ We can see that both equations have the same coefficients for $x$ and $y$, but different constant terms. This suggests that the lines represented by these equations are parallel.Compare slopes of lines: To confirm if the lines are indeed parallel, we can compare the slopes of the two lines. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. Let's convert the first equation to slope-intercept form: $$ 8x + 2y = 14 $$ $$ 2y = -8x + 14 $$ $$ y = -4x + 7 $$ The slope of the first line is $-4$.Convert first equation: Now let's convert the second equation to slope-intercept form: $$ 8x + 2y = 4 $$ $$ 2y = -8x + 4 $$ $$ y = -4x + 2 $$ The slope of the second line is also $-4$.Convert second equation: Since both lines have the same slope but different $y$-intercepts, they are parallel and do not intersect. Therefore, the system of equations has no solutions.

How many solutions does the system have? $\newline$ $\begin{cases} 8x+2y=14 \ 8x+2y=4 \end{cases}$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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How many solutions does the system have?\newline{8x+2y=14 8x+2y=4\begin{cases} 8x+2y=14 \ 8x+2y=4 \end{cases}{8x+2y=14 8x+2y=4​\newlineChoose 111 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\begin{cases} 8x+2y=14 \ 8x+2y=4 \end{cases}$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions