Solving Systems of Equations Graphically

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 two lines to intersect on a graph?

Back

It means that there is a common solution (x, y) that satisfies both equations.

Front

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

Back

Substitute the point into both equations; if both equations are true, it is a solution.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

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

Back

They have no solutions because they never intersect.

Front

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

Back

(1, 3) is the solution.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.