-6.4 x=4y+2.1 ky+3.2 x=5.8 For what value of k does the system of linear equations in the variables x and y have no solutions?

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-6.4 x=4y+2.1  ky+3.2 x=5.8 For what value of  k does the system of linear equations in the variables  x and  y have no solutions?

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Identify Equations Form: Identify the form of the equations and the condition for no solutions. The given system of equations is in the form of a linear system. For a system of two linear equations to have no solutions, the lines represented by the equations must be parallel. This means that the ratios of the coefficients of x and y must be equal, while the constant terms are not proportional.First Equation Slope: Write the first equation in slope-intercept form (y = mx + b). To find the slope of the first equation, we solve for y: -6.4x = 4y + 2.1 4y = -6.4x - 2.1 y = (-6.4/4)x - (2.1/4) y = -1.6x - 0.525 The slope of the first line is -1.6.Second Equation Slope: Write the second equation in slope-intercept form (y = mx + b). To find the slope of the second equation, we solve for y: ky + 3.2x = 5.8 ky = -3.2x + 5.8 y = (-3.2/k)x + (5.8/k) The slope of the second line is -3.2/k.Set Equal Slopes: Set the slopes of the two lines equal to each other to find the value of k that makes the lines parallel. Since the slopes must be equal for the lines to be parallel, we have: -1.6 = -3.2/k Now, solve for k: k = -3.2 / -1.6 k = 2Check Constant Terms: Check if the constant terms are not proportional. For the lines to have no solutions, the constant terms must not be proportional. We have the constant term of the first line as -0.525 and the second line as 5.8/k. Substituting k = 2, we get: 5.8/k = 5.8/2 = 2.9 Since -0.525 is not equal to 2.9, the constant terms are not proportional.

$-6.4 x=4 y+2.1$ $\newline$ $k y+3.2 x=5.8$ $\newline$ For what value of $k$ does the system of linear equations in the variables $x$ and $y$ have no solutions?

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−6.4x=4y+2.1 -6.4 x=4 y+2.1 −6.4x=4y+2.1\newlineky+3.2x=5.8 k y+3.2 x=5.8 ky+3.2x=5.8\newlineFor what value of k k k does the system of linear equations in the variables x x x and y y y have no solutions?

$-6.4 x=4 y+2.1$ $\newline$ $k y+3.2 x=5.8$ $\newline$ For what value of $k$ does the system of linear equations in the variables $x$ and $y$ have no solutions?