Solve Systems: Graphing, Substitution, and Elimination

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 elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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 infinitely many solutions?

Back

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

Front

How do you graph a linear equation?

Back

Identify the y-intercept and use the slope to find another point, then draw a line through the points.

Front

What is the y-intercept of the equation y = mx + b?

Back

The value of y when x = 0, represented by b.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.