Solving Systems by Graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, which represents the values of x and y that satisfy both equations.

Front

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

Back

Write both linear equations in slope-intercept form.

Front

What does it mean if two lines are parallel?

Back

Parallel lines never intersect because they have the same slopes.

Front

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

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating that there is no solution.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you find the x-intercept of a line?

Back

The x-intercept is found by setting y = 0 in the equation of the line and solving for x.

Front

What does it mean if two lines are perpendicular?

Back

Perpendicular lines intersect at a right angle and have slopes that are negative reciprocals of each other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of two or more lines plotted on the same coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where all equations are satisfied.