System of Linear/Quadratic Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so they intersect at every point on that line.

Front

How can you determine the number of solutions in a linear-quadratic system?

Back

By analyzing the intersection points of the linear and quadratic graphs.

Front

What is the general form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of a quadratic equation?

Back

y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the discriminant in a quadratic equation?

Back

It determines the nature of the roots: positive (two real solutions), zero (one real solution), negative (no real solutions).

Front

What is the graphical representation of a linear equation?

Back

A straight line on the coordinate plane.

Front

What is the graphical representation of a quadratic equation?

Back

A parabola on the coordinate plane.