System of Equations 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.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (or curves) on a coordinate plane, where the intersection points represent the solutions.

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the substitution method in 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 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

A system has no solution if 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

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the problem accurately.

Front

What is the cost of a left-handed glove if the total cost of 12 gloves is $561?

Back

The cost of a left-handed glove is $52.