Systems of Linear 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 for a system of equations to have a unique solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The equations represent the same line, so they overlap completely.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point of intersection.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is elimination in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = 5x + 3?

Back

The slope is 5.