Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[4x+y=4],[-6x-y=-6]:} 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.  {:[4x+y=4],[-6x-y=-6]:} One Solution Infinitely Many Solutions No Solutions

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Write Equations: Write down the system of equations to analyze. {:[4x+y=4],[-6x-y=-6]:}Add and Eliminate y: Attempt to solve the system by adding the two equations together to eliminate y. Adding 4x + y = 4 and -6x - y = -6 gives us: 4x + y - 6x - y = 4 - 6 This simplifies to: -2x = -2Solve for x: Solve for x by dividing both sides of the equation by -2. -2x / -2 = -2 / -2 This gives us: x = 1Substitute x into Equation: Substitute x = 1 into one of the original equations to solve for y. Using the first equation 4x + y = 4: 4(1) + y = 4 4 + y = 4 Subtract 4 from both sides to solve for y: y = 4 - 4 y = 0Check Validity: Check the solution (x = 1, y = 0) in the second equation to ensure it is valid. Substitute x = 1 and y = 0 into -6x - y = -6: -6(1) - 0 = -6 -6 = -6 The solution satisfies the second equation as well.Final Solution: Since we have found a single solution (x = 1, y = 0) that satisfies both equations, the system has exactly one solution.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{array}{c} 4 x+y=4 \\ -6 x-y=-6 \end{array}$ $\newline$ 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.\newline4x+y=4−6x−y=−6 \begin{array}{c} 4 x+y=4 \\ -6 x-y=-6 \end{array} 4x+y=4−6x−y=−6​\newlineOne Solution\newlineInfinitely Many Solutions\newlineNo Solutions

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{array}{c} 4 x+y=4 \\ -6 x-y=-6 \end{array}$ $\newline$ One Solution $\newline$ Infinitely Many Solutions $\newline$ No Solutions