Systems of Equations/scatter plots/two table

Solution

to a system means “the point (x,y) where the two lines intersect on a graph” or the (x,y) pair that the two equations would share.

Graphing

– systems set up for graphing will both start with “y = “ [Example: 𝑦 = 2𝑥 − 7 𝑎𝑛𝑑 𝑦 = −3𝑥]

Substitution

systems set up for substitution will have one equation starting with “y=” or “x=” and one in standard form [Example: 4𝑥 − 𝑦 = 9 𝑎𝑛𝑑 𝑦 = −3𝑥 + 1]

- When solving using substitution, “plug in” what y equals to the other equation [Example: 4𝑥 − (−3𝑥 + 1) = 9] - Solve the equation for x. When finished, plug your solution back into either equation for x, to solve for y. - Your final answer will be two numbers in coordinate pair format: (x, y).

Elimination

systems set up for elimination will have both equations in standard form. [Example: 3𝑥 − 2𝑥 = 9 𝑎𝑛𝑑 7𝑥 + 2𝑥 = 10].

-In order to solve using elimination, either the x’s or y’s must “eliminate “ when combining the two equations. - After eliminating one variable, solve for the other. - After solving for one variable, plug the solution back in to either equation to solve for the other. - Your final answer will be two numbers in coordinate pair format (x,y).

Word Problems

when attempting to set up a system of equations from a word problem, follow these steps:

- First, identify the two totals. Put them at the end of the equation, after the equals signs. - Second, identify the variables you need to find and decide how they interact (+, - , x, /) to get your totals. - Third, identify if the variables will have any coefficients in either equation. - Finally, solve using either elimination or substitution, whichever would be more appropriate.

Line of Best Fit

a line that goes through the “middle of the points the best” on a scatter plot. In general, the line should have about the same number of points above it as it does below it.

relative frequency

divide the number in category by the number in the specified total.