12/3 - 12/4 Solving Systems by Graphing

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.

Front

What does it mean for two lines to intersect?

Back

When two lines intersect, it means they cross at a point, which represents the solution to the system of equations.

Front

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

Back

Front

How do you find the x-value of the solution in a system of equations?

Back

To find the x-value of the solution, identify the point where the two lines intersect on the graph and read the x-coordinate.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and never intersect.

Front

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

Back

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

Front

How can you convert an equation to slope-intercept form?

Back

Front

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

Back

Front

What is the graphical representation of a solution to a system of equations?

Back

The graphical representation of a solution is the point of intersection of the lines representing the equations.

Front

How do you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes and positions of the lines: parallel lines (no solution), intersecting lines (one solution), or the same line (infinitely many solutions).