Systems 3x3 and Quadratic-Linear Exit Ticket

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

What does it mean for a system to be consistent?

Back

A consistent system of equations has at least one solution. It can be either a unique solution or infinitely many solutions.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form ax + b = 0, where a and b are constants.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a straight line through the points.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept of the line.

Front

What does it mean for a system to be independent?

Back

An independent system of equations has exactly one solution, meaning the lines represented by the equations intersect at a single point.