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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Solving Systems of Equations - Two Lines

## Parallel and Coincident Equations:

1. If the lines are parallel. There is no solution. The system is inconsistent.

If two lines are parallel, their slopes are equal. m1 = m2

When solving the system by the algebraic Elimination Method if the "letters" vanish and the resulting "sum" is not true, then the two lines are likely parallel with no solution. Always check by solving each equation for the form y = mx + b to see if the slopes are the same but the y-intercepts (b) are different in the two equations

Example 1:

Multiply the first equation by − 2:

Add these equations and note that 0 ≠ 6

 Solve the equation: (1) 2x +3y = 6 and find Solve the equation: (2) 4x +6y = 18 and find

Therefore, the system is Parallel, no solution, inconsistent system.

2. If the lines are coincident. There are infinite solutions. The system is consistent.

When solving the system by the algebraic Elimination Method if the â€œlettersâ€and the â€œnumbersâ€ vanish, which is true, The given equations graph on same line with infinite solutions. Always check by solving each equation for the form y = mx + b to see if both yield the same equation.

Example 2:

Multiply equation (1) by -2