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
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