Math Practice U4 L6

Question

Links to U4 Math Practice L1 - 6 and 9
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Function of the Day:

What do you know?

1.

2.

3.

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5.

6.

7.

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10.

Vocabulary Terms - Define/Illustrate
How many variables are in a linear system of equations?

How do you know if you have a linear system of equations?
What does the solution to a system of linear equations look like?

5 Problems - SHOW ALL WORK!

-A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping.

How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?

-Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks.

What system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?
-The length of a rectangle is equal to triple the width.

Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?



-At the end of the 2000 baseball season, the New York Yankees and the Cincinnati Reds had won a total of 31 World Series. The Yankees had won 5.2 times as many World Series as the Reds.

How many World Series did each team win?
-During the National Football League’s 1999 season, Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders, the Cowboys cornerback. Together they cost the Cowboys $12.867 million.

How much did each player make?



What do I need help with?

Answer 1

Function of the Day:

What do you know?

1. A linear system of equations consists of two or more equations with the same variables.
2. A solution to a system of linear equations is an ordered pair (or tuple) that satisfies all equations in the system.
3. The graphs of linear equations in a system can intersect at different points or be parallel (no solution).
4. Linear equations can be represented in standard form, slope-intercept form, or point-slope form.
5. The number of solutions can be one (intersecting lines), none (parallel lines), or infinitely many (same line).
6. Variables are typically represented by letters (e.g., x, y).
7. A system of linear equations can be solved using substitution, elimination, or graphing methods.
8. A consistent system has at least one solution, while an inconsistent system has no solutions.
9. The point of intersection represents the solution in a graphical representation of linear equations.
10. Linear equations can model real-world scenarios, such as costs, distances, or populations.

Vocabulary Terms - Define/Illustrate

1. Variables: Symbols that represent unknown values in equations (e.g., x, y).
2. Linear equation: An equation that forms a straight line when graphed; typically written in the form y = mx + b.
3. System of equations: A set of equations with the same variables.
4. Solution: A set of values that makes all equations in the system true.
5. Intersecting lines: Lines that cross at a point; represent one unique solution.
6. Parallel lines: Lines that never intersect; represent no solution.
7. Coincident lines: Lines that lie on top of each other; represent infinitely many solutions.

How many variables are in a linear system of equations?

• There can be two or more variables in a linear system of equations, but typically we encounter two (e.g., x and y).

How do you know if you have a linear system of equations?

• A linear system consists of two or more linear equations with the same variables.

What does the solution to a system of linear equations look like?

• The solution is typically represented as an ordered pair (x, y) that satisfies all equations in the system and corresponds to the point of intersection of the graphs of the equations.

5 Problems - SHOW ALL WORK!

1. Pizza Cost Problem: Let \( x \) be the number of toppings.

   For Palanzio’s Pizza:
   Cost = \( 6.80 + 0.90x \)

   For Guido’s Pizza:
   Cost = \( 7.30 + 0.65x \)

   Set the two equations equal: \[ 6.80 + 0.90x = 7.30 + 0.65x \] Subtract \( 0.65x \) from both sides: \[ 6.80 + 0.25x = 7.30 \] Subtract 6.80 from both sides: \[ 0.25x = 0.50 \] Divide both sides by 0.25: \[ x = 2 \] Solution: Palanzio’s Pizza and Guido’s Pizza will cost the same when there are 2 toppings.

2. CD Sales Problem: Let \( l \) = number of CDs sold last week, \( t \) = number of CDs sold this week.

   The system of equations:

   1. \( l = 3t + 6 \) (Last week's sales)
   2. \( l + t = 110 \) (Total sales)

3. Rectangle Dimensions: Let \( l \) = length and \( w \) = width.

   Given: \( l = 3w \) (Length is triple the width) The perimeter \( P = 2l + 2w = 86 \).

   System of equations:

   1. \( l = 3w \)
   2. \( 2l + 2w = 86 \)

4. World Series Wins Problem: Let \( y \) = number of World Series won by the Reds, \( x \) = number won by the Yankees.

   System of equations:

   1. \( x + y = 31 \)
   2. \( x = 5.2y \)

5. NFL Earnings Problem: Let \( a \) = Aikman's earnings, \( d \) = Sanders' earnings.

   System of equations:

   1. \( a = d + 0.467 \)
   2. \( a + d = 12.867 \)

What do I need help with?

• Please identify any specific areas in these topics or problems where you feel confused or need additional clarification!