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Saturday 22nd of October
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Systems of Equations Using Elimination

Objective: Solve systems of linear equations using elimination

Example 1)

 3 x + 2 y = 2-3 x + 2 y = 6 Add the equations 4 y = 8 Simplify y = 8/4 = 2 Substitute using y = 2 3 x + 2(2) = 2 3 x + 4 = 2 Simplify 3 x = -2 x = -2/3 Solution (-2/3, 2)

Example 2)

 - x - y = 8 -2 x - y = -1 Subtract the equations x = 9 Substitute using x = 9 -9 - y = 8 - y = 17 y = -17 Solution (9, -17)

Example 3)

 2 x = -3 y + 1x + 2 y = -1 Rewrite in standard form 2 x + 3 y = 1 x + 2 y = -1 Multiply the 2nd equation by -2 then add 2 x + 3 y = 1 -2 x - 4 y = 2 Simplify -y = 3y = -3 Substitute using y = -3 x + 2(-3) = -1x + -6 = -1 x = 5 Solution (5, -3)

Example 4)

 3 x + 2 y = 12 x - 5 y = -2 Let’s eliminate the x -2(3 x + 2 y ) = -2 (1) 3(2 x - 5 y ) = 3(-2) Multiply the first equation by -2Multiply the 2nd equation by 3 -6 x - 4 y = -26 x - 15 y = -6 Now add. -19 y = -8 y Now substitute Simplify. Solution: