Systems of Equations Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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, so every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

It 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

It involves adding or subtracting equations to eliminate one variable, making it easier to solve.

Front

Write a system of equations based on the following scenario: The cost of 5 apples and 2 bananas is $1.50. The cost of 3 apples and 1 banana is $0.90.

Back

5a + 2b = 1.50 and 3a + 1b = 0.90.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What does it mean for two equations to be dependent?

Back

Dependent equations are those that represent the same line, leading to infinitely many solutions.