S-O-E: Systems of EquationsClick for <Equation SOLVER >


Number of Solutions: (One - None - Infinite)       Different Slope = ONE Answer
       Same Slope, Different Intercept:  (NO SOLUTION) Parallel Lines
       Same Slope, Same Intercept: (INFINITE SOLUTIONS; Same Line)


Solve By Graphing: Y= mx + b Slope Intercept Form:  m = slope, b = Intercept
Ax + By = C Standard Form:  m = -(A)/B and b = C/A
SOLVING For ZERO:  Works well when Coefficients are factors of 'C'.
3x + 2y = 18   and y = x + 4
Line1: when x = 0, y = 9.  When y = 0, x = 6
Line2: When x = 0, y = 4. When y = 0, x = -4
Where do the lines intersect?
 
Substitution: Using a coefficient of '1' for one of the variables.
3x + 2y = 18   and y = x + 4
3x + 2(x + 4) = 18
3x + 2x + 8 = 18
5x = 10
x = 2 ;      y = x + 4 -> y = 2 + 4 -> y = 6
3(2) + 2(6) = 18


Elimination: Make an Equal and Opposite Coefficient