{:[y=0.25 x+12],[y=K(x+3)]:} In the system of equations, K is a constant. For which value of K does the system have no solution? Choose 1 answer: (A) 0 (B) 0.25 (C) 0.75 (D) 12

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{:[y=0.25 x+12],[y=K(x+3)]:} In the system of equations,  K is a constant. For which value of  K does the system have no solution? Choose 1 answer: (A) 0 (B) 0.25 (C) 0.75 (D) 12

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Analyze Equations: Let's analyze the given system of equations: $$ y = 0.25x + 12 $$ $$ y = K(x + 3) $$ For the system to have no solution, the two lines represented by these equations must be parallel. This means they must have the same slope but different y-intercepts. The slope of the first equation is 0.25.Find Slope of Second Equation: Now let's find the slope of the second equation by rewriting it in slope-intercept form (y = mx + b), where m is the slope. $$ y = Kx + 3K $$ The slope of this equation is K.Set Slopes Equal: For the lines to be parallel, their slopes must be equal. Therefore, we set the slope of the first equation equal to the slope of the second equation: $$ 0.25 = K $$Determine Value of K: Since we are looking for the value of K that makes the system have no solution (parallel lines), we can see that K must be 0.25.

`y=0.25x+12` $\newline$ `y=K(x+3)` $\newline$ In the system of equations, $\newline$ $K$ is a constant. For which value of $\newline$ $K$ does the system have no solution? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $0.25$ $\newline$ (C) $0.75$ $\newline$ (D) $12$

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`y=0.25x+12`\newline`y=K(x+3)`\newlineIn the system of equations, \newlineKKK is a constant. For which value of \newlineKKK does the system have no solution?\newlineChoose 111 answer:\newline(A) 000\newline(B) 0.250.250.25\newline(C) 0.750.750.75\newline(D) 121212

`y=0.25x+12` $\newline$ `y=K(x+3)` $\newline$ In the system of equations, $\newline$ $K$ is a constant. For which value of $\newline$ $K$ does the system have no solution? $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $0.25$ $\newline$ (C) $0.75$ $\newline$ (D) $12$