1. Task 2.6 Solving Systems of Equations

2. Solving Systems using Substitution  Solve using Substitution if one variable is isolated!!!  Substitute the isolated variable’s value into the 2 nd equation.  Should have only one variable in the problem now  Solve for the remaining variable  Plug the value of the solved for variable back into one of the original equations to solve for remaining variable.  Example: y= 3x + 2 2x + 2y = 20  2x + 2(3x + 2) = 20  2x + 6x + 4 = 20  8x = 16  X = 2  Then plug back in  Y = 3(2)+ 2  Y = 6 + 2  Y = 8  Solution (2,8)

3. Elimination Method With Same Coefficients  Use elimination if both equations are in standard form  Find a term from each equation with the same variable with the same coefficient.  If the terms have the same sign we subtract one equation from the other. If the terms have different signs we add one equation to another.  Once we have added or subtracted, we now have one variable that we can solve for.  After solving for one variable, plug it into the original equation to solve for the other.  Example: 4x + 3y = 11 2x + 3y = 13  2x = -2  X = -1  4(-1) + 3y = 11  -4 + 3y = 11  3y = 15  Y = 5  Solution (-1, 5)

4. Elimination Method Without Same Coefficients  Pick a variable to eliminate.  Multiply the entire equation(s) by a common multiple of the chosen variable(similar to finding common denominators with adding and subtracting fractions) that we can eliminate.  Find a term from each equation with the same variable with the same coefficient.  If the terms have the same sign we subtract one equation from the other. If the terms have different signs we add one equation to another.  Once we have added or subtracted, we now have one variable that we can solve for.  After solving for one variable, plug it into the original equation to solve for the other.  Example: 4x + 3y = 8 3x – 5y = -23  3(4x + 3y = 8) 4(3x – 5y = -23)  12x + 9y = 24 12x -20y = -92  29y = 116  Y = 4  4x + 3(4) = 8  4x + 12 = 8  4x = -4  X = -1  Solution (-1, 4)