Solving systems by substitution



Solving systems by substitution

Use this method when at least one equation is given with a variable as the ___________________ of the equation |Solving systems by elimination

Use when the equations are in standard form ([pic]) |Solving systems using matrices

Use when the equations are in standard form ([pic]) | |

|Step 1: Take the equation with x or y as the subject and |Goal: To eliminate one of the variables by making the |Step 1: Write the coefficients of the variables in a matrix |

|substitute the right side into the appropriate variable in the |coefficients of x (or y) _____________ and then _______the |[A]. Write the answers to the equations in matrix [B]. |

|2nd equation. |equations. This will _____________one of the variables. | |

| | |Step 2: Enter [A] and [B] in the calculator. |

|Step 2: Solve the 2nd equation. |Step 1: Choose which variable you are going to eliminate | |

| | |Step 3: To solve the matrix equation: [pic], you must solve by |

|Step 3: Take your answer from step 2 and plug it into the first|Step 2: Multiply each equation by the factors needed to create |multiplying |

|equation to find the other variable. |coefficients that are ____________________. | |

| | |___________________. |

|Examples: |Step 3: Solve the remaining equation | |

|1) [pic] | |Step 4: Put [A]-1[B] in your calculator. Answer is [pic]. |

| |Step 4: Take answer from Step 3 and plug it into the first | |

| |equation to find the other variable. |1) [pic] |

| | | |

| |1) [pic] | |

| | | |

| | |2) [pic] |

|2) [pic] | | |

| |2) [pic] | |

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