Algebra Class Quiz: Systems of Equations

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Questions and Answers

What is the sum of the values of x and y for the equation system 3x + 4y = 2 and 5x + 3y + 4 = 0?

  • 10 (correct)
  • 5
  • 9
  • 8 (correct)

If 2x + 5y = 120 and 8x - 9y + 100 = 0 have a solution of (x, y) = (6, 10), what is the value of 4x + 3y?

  • 60
  • 75
  • 85
  • 90 (correct)

What is the coefficient of y in the second equation of the system 3x + 4y = 2 and 5x + 3y + 4 = 0?

  • -3
  • 4
  • 0
  • 3 (correct)

In the provided examples, if the equations are rearranged into the form y = mx + b, what will be the slope (m) when solving for y in 2x + 5y = 120?

<p>-0.4 (A)</p> Signup and view all the answers

What does the presence of a term like +100 in the equation 8x - 9y + 100 = 0 imply about y when solving for it?

<p>y can take on any real value. (C)</p> Signup and view all the answers

Which pair of values is a solution for the equation $2x + 3y = 17$?

<p>(x=4, y=3) (C)</p> Signup and view all the answers

What is the resulting value of y when x = 2 in the equation $5x + 2y = 16$?

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

Which solution pair did not satisfy the equation $9x - 8y = 12$?

<p>(x=6, y=7) (A)</p> Signup and view all the answers

Which equation corresponds to the solution (x=3, y=2)?

<p>$x + y = 16$ (C)</p> Signup and view all the answers

Which of the following equations contains no solutions among the given pairs?

<p>$10x + 15y = -5$ (A)</p> Signup and view all the answers

Flashcards

Simultaneous linear equations

A set of two or more linear equations with the same variables.

Solving two equations with two unknowns

Finding the values of x and y that satisfy both equations in the system.

Linear equation

An equation in which the highest power of each variable is 1.

System of equations

A group of two or more equations considered together.

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Solution (x, y)

A pair of values (x,y) that satisfy both linear equations in a system.

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Simultaneous Linear Equations in Two Variables

Two or more linear equations that must be solved together to find a common solution (x and y values) that satisfies all equations.

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Solution to a System

A set of values for x and y that make all equations in the system true.

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System of Equations Example

A group of two or more equations that have the same variables.

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Solving Simultaneous Equations

Finding the values of variables that satisfy multiple equations at the same time.

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