6-5 Systems of Equations (Graphs and Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

It means that there are no values for the variables that can satisfy all equations in the system.

Front

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

Back

It means that there are an unlimited number of values for the variables that satisfy all equations in the system.

Front

How can 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, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

It involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

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

Back

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

Front

How do you find the intersection point of two lines graphically?

Back

The intersection point is where the two lines cross on the graph.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.