Explanation for Question 35 From the Math (Calc) Section on the Official Sat Practice Test 10
Now for question number 35, we've got this equation here, 2 which says a times X plus B is equal to four X plus 10. 3 We're told the a and B are Constance. And that just means that they're 4 normal numbers and a will always be the same number. 5 And B will always be the same number as well. 6 Not the A's is the same number to be, but the a as a 7 number will never change and B as a number will never change. 8 And so we want to know if this equation has infinitely many solutions, 9 infinitely many solutions, what is the value of B? 10 Right. So we need to think about what does it mean for two lines 11 to have infinitely many solutions? 12 And what it means is that these two lines say one in orange, 13 and then another one also in red, they always overlap each other. 14 Infinitely, infinitely many solutions means that they're the same line, 15 which means that they have to have the same slope and the same 16 Y intercept. All right. 17 So we need to create a situation in which a and B create a 18 line equation that has the same slope, 19 which is four that has a slope of four and a Y intercept of 20 10. So to do that, 21 I'm going to first distribute this a over. 22 So I get my new equation, a X plus B is equal to four 23 X plus 10. Whenever that shows up, 24 there we go. All right. And so I told you that we want the 25 same slope, right? This one has a slope of four. 26 This one has a variable. So since I want a slope of four, 27 cause I need them to be the same. That tells me ...