Solve Systems 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 on a graph.

Front

How do you solve a system of equations by graphing?

Back

To solve by graphing, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This point is the solution to the system.

Front

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

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

Front

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

Back

If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system.

Front

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

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves. A positive slope rises, while a negative slope falls.

Front

What is the setup fee in a cost equation?

Back

The setup fee is a fixed cost that does not change with the number of items produced or purchased, represented as a constant in the equation.

Front

How do you represent a real-world problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure they reflect the situation accurately.

Front

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

Back

The solution is (1, 3).