Systems Graphing & Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean to solve a system of equations graphically?

Back

To solve a system of equations graphically means to plot the equations on a graph and identify the point(s) where they intersect, which represents the solution.

Front

What is substitution in solving equations?

Back

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

Front

How do you identify the solution of a system of equations from a graph?

Back

The solution of a system of equations is identified as the coordinates of the point where the graphs of the equations intersect.

Front

What is the slope-intercept form of a linear equation?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a line?

Back

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.