Systems of Equations (Substitution)

Front

What is a system of equations?

Back

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

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.

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

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 does it mean if a system of equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you find the point of intersection of two lines?

Back

By solving the system of equations to find the values of the variables.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.