Systems of Equations/Inequalities Staar 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 solution to be a feasible solution in a system of inequalities?

Back

A feasible solution is a set of values that satisfies all the constraints (inequalities) in a system.

Front

How do you represent a budget constraint using an inequality?

Back

You can represent a budget constraint using an inequality by stating that the total cost must be less than or equal to the budget. For example, if roses cost $3 each and carnations cost $2 each, the inequality would be 3x + 2y ≤ budget.

Front

What is the difference between '<' and '≤' in inequalities?

Back

The symbol '<' means 'less than' and does not include the boundary, while '≤' means 'less than or equal to' and includes the boundary.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Shade the region that satisfies the inequality.

Front

What is the purpose of finding the intersection of two equations?

Back

Finding the intersection of two equations helps to determine the solution to the system, which is the point where both equations are satisfied.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect and have no solution.

Front

What is a break-even point in a business context?

Back

The break-even point is the level of sales at which total revenue equals total costs, resulting in neither profit nor loss.

Front

How can you express the cost of tickets for different sections of a stadium?

Back

If lower deck tickets cost $42 each and upper deck tickets cost 75% of that, then upper deck tickets cost $31.50 each.

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients represent the rate of change of the variables in the equations and affect the slope of the lines when graphed.