Lesson 16

Elimination

  • Let’s learn how to check our thinking when using elimination to solve systems of equations.

16.1: Which One Doesn’t Belong: Systems of Equations

Which one doesn’t belong?

A:

\(\begin{cases} 3x+2y=49 \\ 3x + 1y = 44 \\ \end{cases}\)

B:

\(\begin{cases} 3y-4x=19 \\ \text{-}3y + 8x = 1 \\ \end{cases}\)

C:

\(\begin{cases} 4y-2x=42 \\ \text{-}5y + 3x = \text{-}9 \\ \end{cases}\)

D:

\(\begin{cases} y=x+8 \\ 3x + 2y = 18 \\ \end{cases}\)

16.2: Examining Equation Pairs

Here are some equations in pairs. For each equation:

  • Find the \(x\)-intercept and \(y\)-intercept of a graph of the equation.

  • Find the slope of a graph of the equation.

  1. \(x + y = 6\) and \(2x + 2y = 12\)
  2. \(3y - 15x = \text{-}33\) and \(y - 5x = \text{-}11\)
  3. \(5x + 20y = 100\) and \(4x + 16y = 80\)
  4. \(3x - 2y = 10\) and \(4y - 6x = \text{-}20\)
  5. What do you notice about the pairs of equations?
  6. Choose one pair of equations and rewrite them into slope-intercept form (\(y = mx + b\)). What do you notice about the equations in this form?

16.3: Making the Coefficient

For each question,

  • What number did you multiply the equation by to get the target coefficient?
  • What is the new equation after the original has been multiplied by that value?
  1. Multiply the equation \(3x + 4y = 8\) so that the coefficient of \(x\) is 9.
  2. Multiply the equation \(8x + 4y = \text{-}16\) so that the coefficient of \(y\) is 1.
  3. Multiply the equation \(5x - 7y = 11\) so that the coefficient of \(x\) is -5.
  4. Multiply the equation \(10x - 4y = 17\) so that the coefficient of \(y\) is -8.
  5. Multiply the equation \(2x + 3y = 12\) so that the coefficient of \(x\) is 3.
  6. Multiply the equation \(3x - 6y = 14\) so that the coefficient of \(y\) is 3.

Summary