[Video] Q3: X/y = 6 4( y + 1) = x if (x, y) is the solution to the system of equations above, what is the value of y ?

Explanation for Question 3 From the Math (No Calc) Section on the Official Sat Practice Test 4

Now a number three, we're given two equations, 2 top equation and a bottom and a quick equation and were told that X 3 comma, Y is the solution to the systems of equations. 4 And then our question that we're being asked is what is the value of 5 Y? So essentially all they want us to do here is solve for Y. 6 And that shouldn't be too tough because if we look here, 7 this bottom equation is perfectly set up for substitution so 8 we can solve the systems of equations. 9 Right? And so what I mean by that is that we already have X 10 solve for, so I can plug X into the numerator of my top equation. 11 And then from there, my only variable in the equation is Y. 12 And that allows me to solve for the value of Y right? 13 So let's rewrite the equation, but instead of writing X, 14 alright, for Y plus one over Y is equal to six. 15 Now I'll distribute that four for Y plus four over 16 wise, equal to six. And now I need to get that Y out of 17 the denominator of my fraction. So I'm going to write six over one to 18 make this more clear, and I'm going to cross multiply that way. 19 I get the Y out of the denominator. So I have four Y plus 20 four is equal to six. Y that's much better, 21 right? So now I'll solve for Y by subtracting for a Y from both 22 sides. Look at four is equal to two Y to solve for Y I 23 simply need to divide by two. Now I get that two is equal to 24 Y, and that makes my answer, answer choice. 25 A and so I just want to give you a bit of advice for 26 systems of equations problems. If you're solving for Y you want to plug 27 in X, you essentially want to plug in your opposite variable that way you 28 only have to solve once and solve for the, 29 for the variable you're interested in, because in some cases you might solve for 30 X first and then solve for Y, but that wastes a little bit of 31 time. 32 So it's always good to try to plug in the opposite variable of what 33 you're looking for.