Module 6 Review (systems)

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 solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation is the intersection point(s) of the lines on a coordinate plane.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true.

Front

How can you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the method of elimination in solving systems of equations?

Back

The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships and conditions into equations, and write them as a system.

Front

What is the solution to the system of equations: -9x - 4y = -20 and 5x + 4y = 4?

Back

The solution is (4, -4).

Front

If a system of equations has infinitely many solutions, what does that imply about the equations?

Back

It implies that the equations represent the same line, meaning they are dependent.