Question
how to solve a system of equations using elimination?
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Answered by
GPT 3.5
To solve a system of equations using elimination, follow these steps:
1. Write the system of equations in standard form with all variables on the left side and constant terms on the right side.
2. Check the coefficients of either the x or y terms in both equations. If they have opposite coefficients (one positive and one negative or vice versa), move to step 3. If not, multiply one or both equations with suitable numbers to obtain opposite coefficients.
3. Add or subtract the two equations together to eliminate one variable. This will result in a new equation with only one variable.
4. Solve the new equation for the remaining variable.
5. Substitute the value of the remaining variable into one of the original equations and solve for the other variable.
6. Check the solution by substituting the values of both variables into both original equations. If the solution satisfies both equations, it is correct. If not, recheck the steps above for any errors.
7. Write the solution as an ordered pair (x, y), where x is the value of one variable and y is the value of the other variable.
Note: If eliminating one variable does not result in a new equation with only one variable, repeat steps 2-4 or use a different method to solve the system.
1. Write the system of equations in standard form with all variables on the left side and constant terms on the right side.
2. Check the coefficients of either the x or y terms in both equations. If they have opposite coefficients (one positive and one negative or vice versa), move to step 3. If not, multiply one or both equations with suitable numbers to obtain opposite coefficients.
3. Add or subtract the two equations together to eliminate one variable. This will result in a new equation with only one variable.
4. Solve the new equation for the remaining variable.
5. Substitute the value of the remaining variable into one of the original equations and solve for the other variable.
6. Check the solution by substituting the values of both variables into both original equations. If the solution satisfies both equations, it is correct. If not, recheck the steps above for any errors.
7. Write the solution as an ordered pair (x, y), where x is the value of one variable and y is the value of the other variable.
Note: If eliminating one variable does not result in a new equation with only one variable, repeat steps 2-4 or use a different method to solve the system.
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