Linear Systems

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Linear Systems

Slope(m)

Finding Slope

Slope Formula

y2-y1 _____ x2-x1

Slope= Undefined when line is vertical

Slope = 0 when line is horizontal

Linear Equations

Standard Form

Standard Form to Slope Intercept Form

Isolate y

Move everything to the right side of the = sign except y

Numbers sign changes when moved over = sign

2x+y=8

y=-2x+8

Ax+By=C

A,B,C = Constants (Only Whole Numbers)

Slope Intercept Form

x,y=variables

x = independent variable

y = dependent variable

b=y intercept

m=slope

What is a Linear System

Constant rate of change

Lines are always straight

System made of 2 or more lines

Solving Linear Systems

Elimination

Convert both equations to Standard Form

Ax+By=C

Choose a variable to eliminate

Multiply both equations by a number to make the coefficients same or opposite

Add/Subtract the equations to eliminate the chosen variable

Sub in value of variable that you solved to find the other variable

Graphing

Make both equations Slope Intercept Form

y=mx+b

Start each line at y-int(b)

Use the equation of the slope to draw the lines

If slope is positive, line increases from left-right

If slope is negative, line decreases from left-right

Substitution

Solve for a variable by rearranging to make everything = a variable

Sub in value of variable that you solved to find the other variable