-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 variable and y have no solutions?

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Write Equations: First, let's write the system of linear equations in standard form: 1) -6.4x - 4y = 2.1 2) 3.2x + ky = 5.8Check Parallel Lines: To find the value of k for which there are no solutions, we need to look for a condition where the two lines represented by the equations are parallel. Two lines are parallel if their slopes are equal.Find Slope Equation 1: The slope of a line in the form Ax + By = C is -A/B. Let's find the slope of the first equation: slope of equation 1) = -(-6.4)/-4 = 6.4/4 = 1.6Find Slope Equation 2: Now let's express the second equation in slope-intercept form to find its slope: 3.2x + ky = 5.8 ky = -3.2x + 5.8 y = (-3.2/k)x + (5.8/k) The slope of equation 2) is -3.2/k.Set Equal Slopes: For the system to have no solutions, the slopes of the two lines must be equal and their y-intercepts must be different. Therefore, we set the slopes equal to each other: 1.6 = -3.2/kSolve for k: Now we solve for k: k = -3.2/1.6 k = -2Verify Y-Intercepts: We have found the value of k. However, we must also ensure that the y-intercepts of the two lines are different for there to be no solutions. The y-intercept of the first equation is 2.1/-4, and the y-intercept of the second equation with k = -2 is 5.8/-2. Since these y-intercepts are different, our condition for no solutions is satisfied.

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