Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[x+6y=1],[-2x-12 y=-3]:} One Solution Infinitely Many Solutions No Solutions

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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.  {:[x+6y=1],[-2x-12 y=-3]:} One Solution Infinitely Many Solutions No Solutions

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Analyze Equations Relationship: Analyze the system of equations to determine the relationship between the two equations. The system of equations is: 1) x + 6y = 1 2) -2x - 12y = -3 We can observe that the second equation is a multiple of the first equation. If we multiply the first equation by -2, we should get the second equation.Multiply and Compare Equations: Multiply the first equation by -2 and compare it to the second equation. Multiplying the first equation by -2 gives us: -2(x + 6y) = -2(1) -2x - 12y = -2 Now we compare this result to the second equation: -2x - 12y = -3 We notice that the coefficients of x and y are the same in both equations, but the constants are different.Determine Solution Type: Determine the type of solution based on the comparison. Since the coefficients are the same but the constants are different, the two lines represented by these equations are parallel and will never intersect. Therefore, the system has no solutions.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{aligned} x+6 y & =1 \\ -2 x-12 y & =-3 \end{aligned}$ $\newline$ One Solution $\newline$ Infinitely Many Solutions $\newline$ No Solutions

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