Explanation for Question 8 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question eight gives us the expression to a X minus 15 is equal to 2 three times X plus five plus five times X minus one. 3 And the equation above a is a constant, 4 if no value of X satisfies the equation, 5 what is the value of a? 6 So the first key thing to note here is no value of X 7 satisfies the equation that happens when there is 8 no way in which this left side is going to be equal to this 9 right side. Another way to think about it is this, 10 that if you picture this left side as align and you picture this 11 right side as another line, 12 they will never intersect. So these are just two arbitrary lines, 13 but let's say they'll never intersect. 14 And we know that two lines never intersect if they have the same slope. 15 So we're going to try and solve through this expression to get them to 16 have the same slope, which would mean that the, 17 the coefficient multiplied by the X would be the same on each side, 18 but the Y intercept might be different. 19 So if you think of point-slope form, Y equals MX plus B, 20 the M one is going to be equal to M two. 21 So the M from this side of the equation, 22 the coefficient in front of the X is going to be equal to the 23 coefficient on the red side of the equation. But we don't know anything about 24 B MI Y intercept should be different. 25 And in fact, if the y-intercept was the same, then we have an infinite 26 number of solutions. So all values of X would satisfy the equation. 27 So that's not what we're looking for. ...