Graphing Systems of Equations

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

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

Back

To find the solution graphically, plot each equation on the same set of axes and identify the point(s) where the lines intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

Front

What does it mean if two lines coincide in a system of equations?

Back

If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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 of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What does the y-intercept represent in a linear equation?

Back

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