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Solving Systems of Equations in Two Variables

Learn methods like graphing, substitution, and elimination to find solutions for systems of linear equations in two variables. Verify solutions by checking equations. Understand different scenarios like intersecting, parallel, and identical lines.

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Solving Systems of Equations in Two Variables

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  1. Section 4.1 Solving Systems of Linear Equations in 2 Variables

  2. Vocab • A System of Equations is a group of 2 or more equations. • The Solution to a system is the order set of numbers that makes all of the equations true. • To Check a Solution, substitute the variables in for x and y into EACH equation and verify. IF all equations work out, then it is a solution

  3. To Solve by GRAPHING: • 1. Graph both equations on the same coordinate plane. • 2. The solution is the point where the 2 lines intersect.(Consistent with independent equations) • 3. If the lines are parallel, there is no solution.(Inconsistent system) • 4. If the lines are identical, there are infinitely many solutions.(Consistent with dependent equations)

  4. To Solve by SUBSTITUTION: • 1. Select one equation and isolate one of the variables. • 2. In the other equation, substitute the expression for step 1 for that variable. • 3. Solve this new equation. • 4. Substitute the value found in step 3 into the first equation to find the other variable. • 5. Check the solution in the original equations.

  5. To Solve by ELIMINATION: • 1. Write both equations in standard form. • 2. Multiply one or both equations so that either x or y have OPPOSITE coefficients. • 3. Add the equations together to eliminate a variable • 4. Solve the resulting equation. • 5. Substitute the value found in step 4 into the either of the original equations to find the other variable. • 6. Check the solution in the original equations.

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