Topic 4 Test Review

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 on a graph.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect. This point is the solution to the system.

Front

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

Back

It means the lines representing 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

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for 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 is the significance of a solid line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with ≤ or ≥.

Front

What is the significance of a dashed line when graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, used for inequalities with < or >.

Front

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

Back

Substitute the coordinates of the point into each equation. If it satisfies all equations, it is a solution.

Front

What is the first step in solving a word problem involving systems of equations?

Back

Identify the variables and write the equations based on the relationships described in the problem.