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Lesson 16

Elimination

Let’s learn how to check our thinking when using elimination to solve 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:

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

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.

$x + y = 6$ and $2x + 2y = 12$
$3y - 15x = \text{-}33$ and $y - 5x = \text{-}11$
$5x + 20y = 100$ and $4x + 16y = 80$
$3x - 2y = 10$ and $4y - 6x = \text{-}20$
What do you notice about the pairs of equations?
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?

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?

Multiply the equation $3x + 4y = 8$ so that the coefficient of $x$ is 9.
Multiply the equation $8x + 4y = \text{-}16$ so that the coefficient of $y$ is 1.
Multiply the equation $5x - 7y = 11$ so that the coefficient of $x$ is -5.
Multiply the equation $10x - 4y = 17$ so that the coefficient of $y$ is -8.
Multiply the equation $2x + 3y = 12$ so that the coefficient of $x$ is 3.
Multiply the equation $3x - 6y = 14$ so that the coefficient of $y$ is 3.