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 is the graphical representation of the equation y = mx + b?

Back

A straight line with slope m and y-intercept b.

Front

How do you find the slope of a line from its equation?

Back

The slope is the coefficient of x in the equation y = mx + b.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, indicating no solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, indicating infinitely many solutions.

Front

How can you determine the solution of a system of equations graphically?

Back

By identifying the intersection point of the two lines on the graph.

Front

What is the y-intercept of the line y = 2x + 1?

Back

1, which is the point where the line crosses the y-axis.

Front

What is the slope of the line represented by the equation y = 4x - 1?

Back

4, indicating the line rises 4 units for every 1 unit it moves to the right.