Linear Systems

Solving Linear Systems

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

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 negative, line
decreases from left-right

If slope is positive, line increases from left-right

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

System made of 2 or more lines

Constant rate of change

Lines are always straight

Slope Intercept Form

y=mx+b

m=slope

b=y intercept

x,y=variables

y = dependent variable

x = independent variable

Standard Form

Ax+By=C

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

x,y=variables

x = independent variable

y = dependent variable

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

Slope = 0 when line is horizontal

Slope= Undefined when line is vertical

Finding Slope

Slope Formula

y2-y1
_____
x2-x1