Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What does the graph of intersecting lines represent in a system of equations?

Back

It represents a unique solution where the lines cross at one point.

Front

What does the graph of parallel lines indicate about a system of equations?

Back

It indicates that there is no solution, as the lines never intersect.

Front

What does it mean if two equations represent the same line when graphed?

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Front

How can you determine the solution to a system of equations by graphing?

Back

By plotting both equations on the same graph and identifying the point(s) where they intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The lines intersect at this point.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3, indicating the line rises 3 units for every 1 unit it moves to the right.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

The y-intercept is 5, which is the point where the line crosses the y-axis.

Front

How do you find the x-intercept of an equation?

Back

Set y to 0 and solve for x.