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


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

Solve by Guessing:
In a multiple choice test where they provide possible solutions, Try the values for (X, Y) into the problem and see which solution solves BOTH Equations.
Also, remember that some problems can only have WHOLE Unit answers. You cannot have 3.5 boys 

Solve By Graphing: 
Y = mx + b Slope Intercept Form:  m = slope, b = Intercept (Y = b when x = 0)
Ax + By = C Standard Form:  m = -(A)/B and b = C/A
While a graph may be a line, and mathematically any point (X, Y) on the line will solve the equation, some problems can only have Whole Unit answers.

SOLVING For ZERO:  This method works well when Coefficients (A and B) are factors of 'C'.
Line1: 3x + 2y = 18   and Line2: 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
Plot the lines. Where do the lines intersect?
 
Substitution: Using a coefficient of '1' for one of the variables.
Line1: 3x + 2y = 18   and Line2: y = x + 4
3x + 2(x + 4) = 18 (substitute: x + 4 for the variable 'y')
3x + 2x + 8 = 18 (distribute)
5x + 8 = 18 (combine and solve)
5x = 10 (Move: Numbers to One Side. Undo + or -)
Solve by Division or Multiplication
5x/5 = 10/5
x = 2 ;     
Plug back in: y = x + 4 -> y = 2 + 4 -> y = 6
CHECK: 3(2) + 2(6) = 18 --> 6 + 12 = 18 --> 18 = 18


Elimination: Make an (INVERSE) Equal and Opposite Coefficient

Classic SOE problems:
Coin Problems
Mixture Problems
Age Problems
Rate and Distance Problems 

Revised: April 24, 2024