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

Solving a system of equations graphically involves plotting the equations on a graph and identifying 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 is the coordinates of the point where the two lines intersect on the graph.

Front

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

Back

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates 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 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 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.