2024 Semester Review Part I

Front

Solve the equation algebraically: |3x + 5| = 1

Back

x = -4/3 or x = -2

Front

A group of 42 people go to an amusement park. The admission price for adults is $16 and for children is $12. They spent $568. How many adults and children were in the group?

Back

Adults: 16, Children: 26

Front

Solve the system using elimination: 4x + 3y = -2 and -12x - 9y = 6

Back

Infinitely Many Solutions

Front

Determine the number of solutions for the system: 3x – 2y = 16 and 6x = 4y + 28

Back

No solution

Front

What is the definition of an absolute value equation?

Back

An equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables, representing a region on a graph.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where the values of the variables satisfy all equations.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into each equation to see if it satisfies all equations.