Algebra 1 Unit 6 Test
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Questions and Answers

What are the two equations that could determine how many children's and adult's tickets were sold?

6X + 2Y = 750, X + Y = 175

What are the two numbers if their sum is 45 and their difference is 21?

(33, 12)

Coinciding lines have _____________ solutions.

infinitely many

Parallel lines have _______________ solutions.

<p>no</p> Signup and view all the answers

Intersecting lines have _______________ solution.

<p>one</p> Signup and view all the answers

The first step for substitution is you either solve for ___________ or ___________.

<p>X, Y</p> Signup and view all the answers

What is the solution of the two equations: A. Y = -8X -10 B. -8X - Y = 10?

<p>infinitely many solutions</p> Signup and view all the answers

What is the solution for the system of equations: A. 3X + Y = -5 B. X = -2?

<p>(-2, 1)</p> Signup and view all the answers

What is the solution for the system of equations: A. X + 2Y = 8 B. Y = -X +7?

<p>(6, 1)</p> Signup and view all the answers

The standard form is always _______________ and no __________________.

<p>simplified, fractions</p> Signup and view all the answers

What is the solution using elimination for the equations: A. 3X - 4Y= -2 B. 6X - 8Y = -4?

<p>infinitely many solutions</p> Signup and view all the answers

What is the solution using elimination: A. Y = 3X -12 B. Y= -2X + 3?

<p>(3, -3)</p> Signup and view all the answers

Solutions are where the shading __________________.

<p>overlaps</p> Signup and view all the answers

Dashed lines indicate: < LESS THAN > GREATER THAN

<p>true</p> Signup and view all the answers

Solid lines indicate: < LESS THAN OR EQUAL TO, > GREATER THAN OR EQUAL TO

<p>true</p> Signup and view all the answers

Shade above for: > GREATER THAN, GREATER THAN OR EQUAL TO

<p>true</p> Signup and view all the answers

Shade below for: < LESS THAN, LESS THAN OR EQUAL TO

<p>true</p> Signup and view all the answers

What are the possible solutions for: A. Y < 1/2X +1 B. Y (GREATER THAN OR EQUAL TO) -3X -1?

<p>(3,1) (2,1) (5,3) (4,0)</p> Signup and view all the answers

What are the steps for creating systems of equations?

<ol> <li>How many unknowns do you have? 2. Assign each unknown value a variable (X and Y) 3. Write the equations based on the scenario. 4. Solve for the specific answer if asked.</li> </ol> Signup and view all the answers

What are the equations to determine the individual price of shorts and sunglasses?

<p>2X + Y = 50, X + 3Y = 50</p> Signup and view all the answers

Write a system of linear equations to determine two numbers if twice a number added to another is 18 and four times the first number minus the other is 12.

<p>2X + Y = 18, 4X - Y = 12</p> Signup and view all the answers

What are the equations to determine how many dimes are in a jar filled with nickels and dimes?

<p>X + Y = 72, 0.5X + 0.10Y= 5.60</p> Signup and view all the answers

What are the steps for solving systems by graphing?

<ol> <li>Graph both equations on the same graph using slope-intercept form. 2. Intersection point is the solution if the lines intersect. 3. If lines are parallel, there is no solution. 4. If equations create the same line, there are infinitely many solutions.</li> </ol> Signup and view all the answers

Intersecting lines have ____________ solutions.

<p>one</p> Signup and view all the answers

Parallel lines have ____________ solutions.

<p>no</p> Signup and view all the answers

Coinciding lines have ____________ solutions.

<p>infinitely many</p> Signup and view all the answers

What is the slope of the line Y = -4X + 5?

<p>-4</p> Signup and view all the answers

What is the Y-intercept of Y = 2X -6?

<p>-6</p> Signup and view all the answers

Write the equation Y - 3X = 5 in slope-intercept form.

<p>Y = 3X + 5</p> Signup and view all the answers

What is 5X + Y = -2 written in slope-intercept form?

<p>Y = -5X - 2</p> Signup and view all the answers

What is the slope of the line -6X + 2Y = 3?

<p>3</p> Signup and view all the answers

What is the slope of the line 4X - 2Y = 8?

<p>2</p> Signup and view all the answers

What is Y + X = 3 in slope-intercept form?

<p>Y = -X + 3</p> Signup and view all the answers

What type of function has a straight line graph?

<p>linear functions</p> Signup and view all the answers

What is the slope of two parallel lines?

<p>same slope</p> Signup and view all the answers

Which is a method of solving systems of equations?

<p>All of the above</p> Signup and view all the answers

Which method would be best used to solve the system: Y = -2X + 8, Y = X + 3?

<p>substitution</p> Signup and view all the answers

Which method would be best used to solve the system: Y = 4X + 8, X = 3?

<p>substitution</p> Signup and view all the answers

Which method would be best used to solve the system: 3X - 2Y = 8, 5X + 2Y = 3?

<p>elimination</p> Signup and view all the answers

Which method would be best used to solve the system: 4X - 8Y = 8, 5X + 2Y = 3?

<p>elimination</p> Signup and view all the answers

What is the value of X to the solution: 4X - 2Y = 8, 5X + 2Y = 10?

<p>2</p> Signup and view all the answers

What is the value of Y to the solution: 3X - 2Y = 2, -3X + 5Y = -8?

<p>-2</p> Signup and view all the answers

What is the value of X to the solution: 3X - 2Y - 2, Y = 11?

<p>8</p> Signup and view all the answers

What is the value of Y to the solution: X + 5Y = 14, X = Y + 2?

<p>2</p> Signup and view all the answers

What is the solution to this system of linear equations: X + 5Y =18, X=3?

<p>(3, 3)</p> Signup and view all the answers

What is the solution to this system of linear equations: 2X + Y = 18, Y = 3X -2?

<p>(4, 10)</p> Signup and view all the answers

What is the solution to this system of linear equations: 2X + Y = 2, -2X - 3Y= 10?

<p>(4, -6)</p> Signup and view all the answers

What is the solution to this system of linear equations: 2X + Y = 3, -X - Y = -1?

<p>(2, -1)</p> Signup and view all the answers

What is the solution to this system of linear equations: 3X + 4Y = 3, -X - 5Y = 10?

<p>(5, -3)</p> Signup and view all the answers

Study Notes

Systems of Equations

  • Movie ticket prices: $6 for adults, $2 for children; total tickets sold = 175, total cash = $750.
  • System of equations:
    • 6X + 2Y = 750
    • X + Y = 175
  • Solution for adult and children's tickets: (100, 75).

Solving for Numbers

  • The sum of two numbers is 45, and their difference is 21.
  • System of equations:
    • X + Y = 45
    • X - Y = 21
  • Solution: (33, 12).

Lines and Solutions

  • Coinciding lines have infinitely many solutions (same line).
  • Parallel lines have no solutions (do not intersect).
  • Intersecting lines have one solution (unique intersection point).

Substitution Method

  • First step in substitution: solve for X or Y.

Elimination Method

  • Eliminating variables can lead to:
    • Infinitely many solutions
    • No solution
    • A unique solution
  • Example solution using elimination: from equations 3X - 4Y = -2 and 6X - 8Y = -4 leads to infinitely many solutions.

Inequalities and Graphing

  • Systems of inequalities must be in slope-intercept form.
  • Graph with solid/dashed lines and shade above or below.
  • Solutions are where shading overlaps; points on solid lines are solutions, points on dashed lines are not.

Slope and Intercepts

  • Slope of line Y = -4X + 5 is -4.
  • Y-intercept of line Y = 2X - 6 is -6.
  • Slope-intercept form is Y = mx + b.

Types of Functions

  • Linear functions produce straight line graphs.
  • Slope of parallel lines is the same.
  • Various methods for solving systems: graphing, substitution, elimination.

Solving Specific Systems

  • Use substitution or elimination based on the situation.
  • Example: Y = -2X + 8 and Y = X + 3 solved by substitution.

System Solutions

  • Solutions can be found for various equations such as:
    • X + 5Y = 18, X = 3 gives (3, 3).
    • 2X + Y = 18, Y = 3X - 2 gives (4, 10).
    • Systems can also yield various values of X and Y depending on the setup.

Conclusion

  • Mastery of systems of equations, inequalities, and their respective solutions is essential in algebra.
  • Equations can model real-world scenarios effectively through structured methods like substitution and elimination.

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Description

Test your knowledge with this Algebra 1 Unit 6 quiz focused on systems of equations. Solve practical problems involving adult and children's movie ticket sales, and learn to set up and solve simultaneous equations. This quiz is designed to enhance your algebraic problem-solving skills.

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