Unit 4 Post Review

Front

What is the x-coordinate of the system of solutions shown on the graph?

Back

The x-coordinate of the system of solutions is the value where the two lines intersect. In this case, it is 2.

Front

If Larry starts with $50 and saves $10 per week, while Michael starts with $30 and saves $15 per week, how can we find out after how many weeks they will have saved the same amount of money?

Back

Set up the equations: Larry's savings: 50 + 10w; Michael's savings: 30 + 15w. Solve for w when both savings are equal.

Front

What is the total revenue generated from selling small and large boxes of chocolates if a small box costs $5 and a large box costs $10?

Back

Total revenue = (number of small boxes * 5) + (number of large boxes * 10). For Tina, this equals $140.

Front

Back

Multiply both sides by 6 to eliminate fractions, then solve for x. The solution is x = 2.4.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value of x that satisfies the equation.

Front

What is the meaning of 'no solution' in a system of equations?

Back

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

Front

What does 'infinitely many solutions' indicate in a system of equations?

Back

It indicates that the two equations represent the same line, so every point on the line is a solution.

Front

How do you determine the number of small and large boxes sold if Tina sold a total of 20 boxes for $140?

Back

Set up the equations: x + y = 20 (total boxes) and 5x + 10y = 140 (total sales). Solve the system of equations.

Front

What is the formula for finding the intersection point of two linear equations?

Back

To find the intersection, set the equations equal to each other and solve for x and y.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of y with respect to x; it shows how steep the line is.