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Solving Systems of Equations Using Substitution Method

This guide provides a step-by-step approach to solving systems of equations using the substitution method. The process begins by solving one equation for one variable, followed by substituting this expression into the other equation. After simplifying and solving for the remaining variable, you substitute back to find the initial variable's value. Finally, it's essential to verify the solution in both original equations to ensure accuracy. Examples with detailed steps illustrate this effective method for solving linear equations.

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Solving Systems of Equations Using Substitution Method

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  1. Solving Systems of Equations using Substitution

  2. 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.

  3. y = 4x and 3x + y = -21 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

  4. y = 4x 3x + y = -21 You found that x = -3 Step 4: Substitute back into either original equation to find the value of the other variable. (if x = -3 then y = ?) 3x + y = -21 3(-3) + y = -21 -9 + y = -21 y = -12 Solution to the system is (-3, -12).

  5. y = 4x 3x + y = -21 Step 5: Check the solution in both equations. Solution to the system is (-3,-12). 3x + y = -21 3(-3) + (-12) = -21 -9 + (-12) = -21 -21= -21 y = 4x -12 = 4(-3) -12 = -12

  6. Want

  7. x + y = 5 and y = 3 + x

  8. Example #2: x + y = 10 and 5x– y = 2 Step 1: Solve one equation for one variable. x + y = 10 y = -x +10 Step 2: Substitute the expression from step one into the other equation. 5x - y = 2 5x -(-x +10) = 2

  9. x + y = 10 and 5x– y = 2 Step 3: Simplify and solve the equation. 5x -(-x + 10) = 2 5x + x -10 = 2 6x -10 = 2 6x = 12 x = 2

  10. x + y = 10 and 5x– y = 2 You found that x = 2 Step 4: Substitute back into either original equation to find the value of the other variable. x + y = 10 2 + y = 10 y = 8 Solution to the system is (2,8).

  11. x + y = 10 5x – y = 2 Step 5: Check the solution in both equations. Solution to the system is (2, 8). 5x – y = 2 5(2) - (8) = 2 10 – 8 = 2 2 = 2 x + y =10 2 + 8 =10 10 =10

  12. Smart Bird

  13. Closure: Solve by substitution

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