Solving Systems of Linear Equations by Graphing and Substitution

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 to solve a system of equations?

Back

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

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

The system has infinite solutions because every point on the line is a solution.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

How do you determine the solution from a graph of two lines?

Back

The solution is the point where the two lines intersect.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x=0.

Front

What is the slope of a line?

Back

The rate of change of y with respect to x, often represented as 'm' in the equation y = mx + b.

Front

How can you tell if a system of equations has one solution?

Back

If the lines representing the equations intersect at exactly one point.