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**Systems of Equations Standards: MCC9-12.A.REI.5-12**

Objectives: To solve systems of linear equations by substitution, elimination and graphing.

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**Solving Systems of Equations using Substitution**

Steps: 1. Solve one equation for one variable (y= ; x= ; a=) 2. Substitute the expression from step one into the other equation. 3. Simplify and solve the equation. 4. Substitute back into either original equation to find the value of the other variable. 5. Check the solution in both equations of the system.

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y = 4x 3x + y = -21 Example Step 1: Solve one equation for one variable. y = 4x (This equation is already solved for y.) Step 2: Substitute the expression from step one into the other equation. 3x + y = -21 3x + 4x = -21 Step 3: Simplify and solve the equation. 7x = -21 x = -3

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**y = 4x 3x + y = -21 Step 4: Substitute back into either original**

equation to find the value of the other variable. 3x + y = -21 3(-3) + y = -21 -9 + y = -21 y = -12 Solution to the system is (-3, -12).

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**Solving Systems of Equations using Elimination**

Steps: 1. Place both equations in Standard Form, Ax + By = C. 2. Determine which variable to eliminate with Addition or Subtraction. 3. Solve for the variable left. 4. Go back and use the found variable in step 3 to find second variable. 5. Check the solution in both equations of the system.

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5x + 3y = 11 5x = 2y + 1 EXAMPLE STEP1: Write both equations in Ax + By = C form x + 3y =1 5x - 2y =1 STEP 2: Use subtraction to eliminate 5x x + 3y = x + 3y = 11 -(5x - 2y =1) x + 2y = -1 Note: the (-) is distributed. STEP 3: Solve for the variable. 5x + 3y =11 -5x + 2y = -1 5y = y = 2

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**The solution to the system is (1,2).**

5x + 3y = 11 5x = 2y + 1 STEP 4: Solve for the other variable by substituting into either equation. 5x + 3y =11 5x + 3(2) =11 5x + 6 =11 5x = 5 x = 1 The solution to the system is (1,2).

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**Solving Systems of Equations By Graphing**

Steps: 1. Graph both lines 2. The point of intersection is the solution 3. If the lines do not intersect (or are parallel), there are NO solutions 4. If the lines are actually the same, there are INFINITE solutions. 5. You do NOT shade equations, only inequalities.

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**Solving Systems of Equations By Graphing**

Solve the following system of equations: y = 2x + 1 y = ½x + 3

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