2. Advanced Algebra
Systems Nonlinear — Quiz
Test your understanding of systems nonlinear with 5 practice questions.
Practice Questions
Question 1
Consider the system of equations: $\begin{cases} y = x^2 - 4x + 4 \ y = x - 2 \end{cases}$. What are the solutions for $(x, y)$?
Question 2
A system of equations consists of a circle with equation $x^2 + y^2 = 10$ and a line with equation $y = x + 2$. What are the $x$-coordinates of the intersection points?
Question 3
Given the system of equations: $\begin{cases} y = x^2 - 6x + 5 \ y = -x + 5 \end{cases}$. What is the sum of the $y$-coordinates of the solutions?
Question 4
A system of equations consists of a parabola $y = x^2 - 2x + 1$ and a line $y = k$. For what value of $k$ will the system have exactly one real solution?
Question 5
Consider the system of equations: $\begin{cases} x^2 + y^2 = 5 \ y = 2x \end{cases}$. What is the product of the $x$-coordinates of the solutions?