{:[8(x-9y)=8-6(x-4)],[4x-Ay=16-3x]:} In the system of equations, A is a constant. For what value of A does the system of linear equations have infinitely many solutions?

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{:[8(x-9y)=8-6(x-4)],[4x-Ay=16-3x]:} In the system of equations,  A is a constant. For what value of  A does the system of linear equations have infinitely many solutions?

Bytelearn · Accepted Answer

Simplify First Equation: First, let's simplify the first equation in the system. 8(x - 9y) = 8 - 6(x - 4) Distribute the 8 and -6 on both sides of the equation. 8x - 72y = 8 - 6x + 24 Combine like terms. 8x - 72y + 6x = 8 + 24 14x - 72y = 32 Now, divide the entire equation by 2 to simplify it further. (14x - 72y) / 2 = 32 / 2 7x - 36y = 16Simplify Second Equation: Next, let's simplify the second equation in the system. 4x - Ay = 16 - 3x Add 3x to both sides of the equation to move all x terms to one side. 4x + 3x - Ay = 16 7x - Ay = 16Check for Infinitely Many Solutions: For the system to have infinitely many solutions, the two equations must be the same, or one must be a multiple of the other. This means that the coefficients of x and y must be proportional, and the constants on the right side of the equation must also be the same. From the simplified equations, we have: 7x - 36y = 16 (from the first equation) 7x - Ay = 16 (from the second equation) For these to be the same, A must be equal to 36.

$\begin{array}{c} 8(x-9 y)=8-6(x-4) \\ 4 x-A y=16-3 x \end{array}$ $\newline$ In the system of equations, $A$ is a constant. For what value of $A$ does the system of linear equations have infinitely many solutions?

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8(x−9y)=8−6(x−4)4x−Ay=16−3x \begin{array}{c} 8(x-9 y)=8-6(x-4) \\ 4 x-A y=16-3 x \end{array} 8(x−9y)=8−6(x−4)4x−Ay=16−3x​\newlineIn the system of equations, A A A is a constant. For what value of A A A does the system of linear equations have infinitely many solutions?

$\begin{array}{c} 8(x-9 y)=8-6(x-4) \\ 4 x-A y=16-3 x \end{array}$ $\newline$ In the system of equations, $A$ is a constant. For what value of $A$ does the system of linear equations have infinitely many solutions?