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Section 4.1

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

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Section 4.1

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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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