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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