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:
\(\begin{cases} 3y4x=19 \\ \text{}3y + 8x = 1 \\ \end{cases}\)
C:
\(\begin{cases} 4y2x=42 \\ \text{}5y + 3x = \text{}9 \\ \end{cases}\)
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.
 \(x + y = 6\) 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 slopeintercept 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?
 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.