Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[x+3y=7],[x-3y=-10]:} 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+3y=7],[x-3y=-10]:} One Solution Infinitely Many Solutions No Solutions

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Analyze Equations: Analyze the system of equations to determine if they are parallel, the same line, or intersecting lines. The system of equations is: x + 3y = 7 x - 3y = -10 We can compare the coefficients of x and y in both equations to determine the relationship between the lines they represent.Compare Coefficients of x: Compare the coefficients of x in both equations. The coefficient of x in the first equation is 1, and the coefficient of x in the second equation is also 1. Since the coefficients of x are the same, the lines are either parallel or the same line.Compare Coefficients of y: Compare the coefficients of y in both equations. The coefficient of y in the first equation is 3, and the coefficient of y in the second equation is -3. Since the coefficients of y are opposites, the lines are not parallel and must intersect.Compare Constants: Compare the constants in both equations. The constant in the first equation is 7, and the constant in the second equation is -10. Since the constants are different, the lines are not the same line.Conclude Number of Solutions: Conclude the number of solutions based on the analysis. Since the lines are not parallel and not the same line, they must intersect at exactly one point. Therefore, the system of equations has exactly one solution.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{array}{l} x+3 y=7 \\ x-3 y=-10 \end{array}$ $\newline$ One Solution $\newline$ Infinitely Many Solutions $\newline$ No Solutions

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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.\newlinex+3y=7x−3y=−10 \begin{array}{l} x+3 y=7 \\ x-3 y=-10 \end{array} x+3y=7x−3y=−10​\newlineOne Solution\newlineInfinitely Many Solutions\newlineNo Solutions

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{array}{l} x+3 y=7 \\ x-3 y=-10 \end{array}$ $\newline$ One Solution $\newline$ Infinitely Many Solutions $\newline$ No Solutions