[Video] Q14: Y x^2 + 3x -7 y - 5x + 8 = 0 how many solutions are there to the system of equations above?

Explanation for Question 14 From the Math (No Calc) Section on the Official Sat Practice Test 8

So question number 14 is asking us how many solutions are there in the 2 system of equations. And so the first thing that we can do is just 3 solve the system of equations, right? Because if we solve it, 4 we'll get a certain number of solutions. And however many solutions we get is 5 going to be our answer. So I can see that have a Y up 6 here, and I have a Y here. And so perhaps a good idea will 7 be to solve for Y in the bottom equation and then plug it into 8 the top equation so I can solve for Y and I'll get that. 9 Y is equal to positive five X minus eight, 10 because I'll add five X to both sides of the equation to subtract eight 11 from both sides of the equation. Now I take this and I plug it 12 in, right? So I have five X minus eight is equal to X squared, 13 plus three X minus seven. 14 And now I just need to combine like terms so that I have a 15 singular, um, a singular quadratic equation. 16 So I'll subtract five X from both sides. I get negative eight is equal 17 to X squared, minus two X minus seven. 18 And then I can add eight to both sides. This will cancel. 19 And now I'm left with one quadratic equation, 20 which is X squared, minus two X plus one. Now you might be tempted 21 to factor this, right, but they asked us how many solutions and 22 the way that you find the number of solutions is by using the quadratic 23 formula, which you might remember is, um, 24 X equals opposite B plus or minus square root B squared minus four, 25 AC all over to a, and what ...