1.7 Solving linear nonlinear systems

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic equation?

Back

An equation of the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is substitution in solving equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If the equations are satisfied, the point is a solution.

Front

What is the graphical method of solving systems of equations?

Back

Graphing each equation on the same set of axes and identifying the points of intersection as solutions.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The discriminant (b² - 4ac) 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 solution set?

Back

The set of all possible solutions to a system of equations.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, found at the coordinates (h, k) in the vertex form y = a(x - h)² + k.