[Video] Q9: Kx - 3y = 4 4x - 5y = 7 in the system of equations above, k is a constant and x and y are variables. for what value of k will the system of equations have no solution?

Explanation for Question 9 From the Math (No Calc) Section on the Official Sat Practice Test 3

Now for question number nine, we're given a systems of equations and we're told 2 that these equations have no solution. 3 And so what we really need to do here is think about what no 4 solution means. And if we think about it in terms of lines, 5 right, we know that that means lines will never intersect because an intersection really 6 is a solution. And if lines are never going to intersect, 7 that means that they are parallel, which in other words means that those two 8 lines have to have the same slope. 9 And if we have the same slope, right, 10 we can think about these two equations. It's not just being, 11 you know, normal equations, but really being equations of lines in standard form. 12 And notice that the bottom equation has all its information, 13 right? We see that we've got a total equation there. 14 And so what we can do here is rewrite this equation, 15 not negative seven, positive seven, and solve for the slope of that equation because 16 whatever that slope is, should be equal to the slope of the top equation. 17 But in order to find the slope, we need to move from standard form 18 to a Y intercept form, which looks like Y equals MX 19 plus B. And so we'll start by moving that Forex over 20 to convert to y-intercept form. And that gives us a negative five, 21 Y is equal to negative four X plus seven. 22 And then the last step is going to be to get rid of that 23 negative five that's on the Y I'll do that by dividing everything by negative 24 five, these negat...