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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