Solving Systems of Equations 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

Two lines intersect when they cross each other at a point, which represents the solution to the system of equations.

Front

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

Back

To find the solution graphically, plot both equations on the same graph and identify the point where they intersect.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

What is the slope of a line?

Back

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

Front

How do you determine the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the values of the variables that satisfy all equations in the system simultaneously.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What does it mean if two lines are coincident?

Back

If two lines are coincident, they lie on top of each other and have infinitely many solutions, as every point on the line is a solution.

Front

How can you identify the y-intercept from an equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the y-intercept is the value of b.