H. Alg II Chap 3 CFA #3

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 to solve a system of equations by substitution?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical method for solving a system of equations?

Back

It involves graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the solution to the system of equations y = -4x + 5 and y = 3x - 16?

Back

(3, -7)

Front

What is the solution to the system of equations 2x + 3y = 6 and 4x + 6y = 12?

Back

No solution (the equations are dependent and represent the same line).

Front

What is the solution to the system of equations 2x + y = 0 and 4x - 2y = 4?

Back

(-2, 1)