System of equations review 11/21/24

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 solution to satisfy a system of equations?

Back

A solution satisfies a system of equations if it makes all the equations true when substituted into them.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

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

A system has no solution if the equations represent parallel lines that 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 represent a word problem as a system of equations?

Back

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

Front

What is the first step in solving a word problem involving ages?

Back

Define the variables for the ages of the individuals involved.