Math 1: Test no. 4 -Systems of Equations and Inequalities

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 no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the graphical method for solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point(s) of intersection represent the solution.

Front

What is the solution to the system of equations 2x - y = 4 and y = -2x + 8?

Back

The solution is (3, 3).

Front

How do you solve the system of equations 2x - y = 0 and 4x - y = 0?

Back

The solution is (0, 0), indicating infinite solutions.

Front

What is the value of x in the solution for the system 2x - y = 4 and y = -2x + 8?

Back

x = 3.