Introduction to Solving Systems Graphically

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 to solve a system graphically?

Back

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

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, plot each equation on the same graph and look for the point(s) where the lines intersect.

Front

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

Back

If two lines are parallel, it indicates that there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphed?

Back

If two lines coincide, it means they are the same line, resulting in infinitely many solutions.

Front

What is the significance of the coordinates (x, y) in the context of a solution to a system of equations?

Back

The coordinates (x, y) represent the values of the variables that satisfy all equations in the system.

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values into each equation. If the equations hold true, the point is a solution.

Front

What is the role of the y-intercept in graphing linear equations?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is zero.