Key Facts for a system of equations?

Question

What're four key facts that an Algebra 1 student must know if they are going to write,graph,solve,and check a system of equations?

Answer 1

(1)  The Cartesian Coordinate System (usually, with an x-axis and a y-axis) may be used to plot linear (and other) equations.  For Algebra I, let’s stick with linear equations.

(2)  Two points determine a line.  Plot the two points as (x,y) and connect them with a line.  Extend the line in each direction.

 

(3)  Equations representing lines may be written in various forms:

       Standard Form:  Ax+By=C

       Slope-intercept form, y=mx + b,  where m is the slope and b is the y-intercept

       Point-slope form,  (y-y₁)=( (y₂-y₁)/(x₂-x₁) )(x-x₁)        where (x₁,y₁) and (x₂,y₂) are points

     . . . (more)

 

(4)  To “solve” a system of equations means to find the point (x,y) that satisfies all the equations in the system.  To Check an Answer:  once an answer is obtained, plug in the values of (x,y) to see if the equations are true. 

 

(extra points) Parallel lines have the same slope, m.  Perpendicular lines have negative, reciprocal slopes.  That is, if the slope of one line is m, then the slope of all perpendicular lines is (-1/m).