Solving Systems by Graphing

Front

What does the standard A1.AREI.6 focus on?

Back

The standard A1.AREI.6 focuses on solving systems of equations, particularly through graphing methods.

Front

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

Back

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

Front

What does it mean if two lines on a graph are the same?

Back

If two lines on a graph are the same, it means they represent the same equation, resulting in infinite solutions for the system.

Front

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

Back

The solution to a system of equations graphically is found at the point where the two lines intersect.

Front

What does it indicate if two lines are parallel on a graph?

Back

If two lines are parallel, it indicates that the system of equations has no solution, as the lines will never intersect.

Front

What is the significance of the point (1,3) in the context of systems of equations?

Back

The point (1,3) is a solution to a specific system of equations, meaning it satisfies both equations in the system.

Front

How can you convert the equation -6x + 3y = 9 into slope-intercept form?

Back

To convert -6x + 3y = 9 into slope-intercept form, isolate y: 3y = 6x + 9, then y = 2x + 3.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines representing the equations are parallel and do not intersect.

Front

What is the graphical representation of a system with infinite solutions?

Back

The graphical representation of a system with infinite solutions is two overlapping lines, indicating they are the same line.

Front

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

Back

The first step in solving a system of equations by graphing is to graph each equation on the same coordinate plane.