# 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.