Systems of Nonlinear Equations 1

Which of the following graphs represents the solutions to the system of equations x is equal to 2 minus y and y is equal to x squared minus 4. So essentially, we want to find the graphs that represent these two equations, and where they intersect represent the solutions. So, let's see. y equals x squared minus 4. That's going to be an upward opening parabola with a y-intercept of negative 4, and we see that is the case. Or I should say the y-coordinate of its vertex would be negative 4 right over there, and also the y-intercept. So that looks like this one right over here. And this is the only one that opens like that, so we can immediately say that this is probably going to be the red one right over here. But we can verify that this line right over here is 2 minus x. So if I were to write this in traditional slope intercept form, I could rewrite this as x is equal to 2 minus y. Add y to both sides. We have y plus x is equal to 2, or y is equal to negative x plus 2. So we see the y-intercept is 2, and its slope is negative 1. So that's indeed this line, and so the solutions here are going to be that point and that point right over here. Red is what represents the solutions to this non-linear system of equations.