{:[ax+by=1],[ax-by=1],[y=c]:} In the system of three linear equations above, a,b and c are constants and b!=0. If the system has exactly one solution, what is the value of c in terms of a and b ?

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{:[ax+by=1],[ax-by=1],[y=c]:} In the system of three linear equations above,  a,b and  c are constants and  b!=0. If the system has exactly one solution, what is the value of  c in terms of  a and  b ?

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Identify Equations: Identify the system of equations. The system of equations is given by: {:[ax+by=1],[ax-by=1],[y=c]:}Conditions for Solution: Determine the conditions for a unique solution. For a system of linear equations to have exactly one solution, the equations must be independent and consistent. This means that no equation can be a multiple of another, and they must intersect at a single point.Eliminate x: Subtract the second equation from the first to eliminate x. (ax + by) - (ax - by) = 1 - 1 This simplifies to: 2by = 0Solve for y: Solve for y. Since b is not equal to 0 (b != 0), we can divide both sides by 2b to find y. y = 0 / (2b) y = 0Compare with Third Equation: Compare the result with the third equation. The third equation states that y = c. Since we found that y = 0 for the system to have a unique solution, we can equate c to 0. c = 0

$\begin{array}{l} a x+b y=1 \\ a x-b y=1 \\ y=c \end{array}$ $\newline$ In the system of three linear equations above, $a, b$ and $c$ are constants and $b \neq 0$ . If the system has exactly one solution, what is the value of $c$ in terms of $a$ and $b$ ?

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