Solving Systems of Equations

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 two lines to intersect on a graph?

Back

It means that the system of equations has a unique solution, which is the point of intersection.

Front

What is the solution to a system of equations?

Back

The values of the variables that satisfy all equations in the system.

Front

What does it mean if two lines are parallel?

Back

It means that the system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines are coincident?

Back

It means that the system of equations has infinitely many solutions, as the lines lie on top of each other.

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on the same coordinate plane.

Front

What is the significance of the point (1,3) in a system of equations?

Back

It is a solution to the system, meaning it satisfies all equations in the system.

Front

What is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

Set the two equations equal to each other to find the value of x.