Solve Systems 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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The system has no solution because the lines never intersect.

Front

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

Back

The system has infinite solutions because every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point (0, 3) on the graph.

Front

How can you find the x-intercept of a linear equation?

Back

Set y to 0 and solve for x.

Front

What is the graphical representation of the equation y = -x + 4?

Back

A straight line with a slope of -1 and a y-intercept at (0, 4).