Systems Review 5.1-5.4

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.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and ensure the equations reflect the conditions given in the problem.

Front

What does the solution to a system of equations represent?

Back

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

Front

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

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method 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

The elimination method 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, and every point on that line is a solution.

Front

How do you check if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If the equations hold true, the point is a solution.

Front

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

Back

Coefficients represent the rate of change of the variables and influence the slope of the lines in a graphical representation.