How many solutions does the system have? {[3x+y=8],[2x+2y=8]:} 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?  {[3x+y=8],[2x+2y=8]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

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Write Equations: Write down the system of equations. We have the following system of equations: $$ \begin{cases}  3x + y = 8 \ 2x + 2y = 8  \end{cases} $$Simplify Second Equation: Attempt to simplify the second equation to see if it is a multiple of the first. Divide the second equation by 2 to simplify it: $$ \frac{2x + 2y}{2} = \frac{8}{2} $$ This simplifies to: $$ x + y = 4 $$Compare Equations: Compare the simplified second equation with the first equation. We now have: $$ \begin{cases}  3x + y = 8 \ x + y = 4  \end{cases} $$ These two equations are not multiples of each other, which means they are not the same line.Determine Intersection: Determine if the two equations intersect. Since the two equations are not the same line and they are both linear equations in two variables, they should intersect at exactly one point unless they are parallel.Check Slopes: Check the slopes of the two lines to determine if they are parallel. The slope of the first equation (3x + y = 8) is -3, and the slope of the second equation (x + y = 4) is -1. Since the slopes are different, the lines are not parallel.Conclude Solutions: Conclude the number of solutions. Because the lines are not parallel and are not the same line, they will intersect at exactly one point. Therefore, the system of equations has exactly one solution.

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 3 x+y=8 \\ 2 x+2 y=8 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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How many solutions does the system have?\newline{3x+y=82x+2y=8 \left\{\begin{array}{l} 3 x+y=8 \\ 2 x+2 y=8 \end{array}\right. {3x+y=82x+2y=8​\newlineChoose 111 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} 3 x+y=8 \\ 2 x+2 y=8 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions