Practice Objectives
- Demonstrate the ability to solve a system of linear equations using substitution
- Demonstrate the ability to solve a system of linear equations using elimination
Practice Solving a Two-Variable Linear System with Substitution and Elimination
Instructions:
Answer 7/10 questions correctly to pass.
Problem:
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The Substitution Method:
- Solve either equation for one of the variables
- Look for a variable with a coefficient of 1 or -1
- Substitute in for that variable in the other equation
- Solve the linear equation in one variable
- Substitute the known value into either original equation and solve for the other unknown
- Check the solution
The Elimination Method:
- Write both equations in standard form
- ax + by = c
- Transform the equations so that the coefficients of one pair of variable terms are opposites
- Find the least common multiple (LCM) of the chosen coefficients
- Multiply both sides of each equation by the necessary numbers to make the chosen coefficients opposites
- Add the two left sides of the equations together, set this equal to the sum of the two right sides of the equations
- This will eliminate one variable
- Solve the linear equation in one variable
- Find the other unknown using substitution
- Check the solution
Step-by-Step:
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$$x = $$
$$y = $$
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