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Solving Linear Equations Using Substitution Method

In this lesson, we explore how to use the substitution method to solve systems of linear equations. We demonstrate the process through examples: rearranging the first equation to isolate variables, substituting them into the second equation, and simplifying the results step by step. For instance, we solve for x and y in the equations x – 2y = -1 and 2x – 3y = 4. This method not only aids in solving but also strengthens understanding of relationships between variables. Follow along to master substitution techniques!

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Solving Linear Equations Using Substitution Method

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  1. Lesson 59Rearranging Before Substitution Ex 59.1 Use substitution to solve for x & y: x – 2y = -1 (first equation) + 2y + 2y x = 2y - 1

  2. Rearranging Before Substitution cont. 2x – 3y = 4 (second equation) 2(2y – 1) – 3y = 4 4y – 2 - 3y = 4 y – 2 = 4 y = 6

  3. Rearranging Before Substitution cont. Ex. 59.2 Use substitution to solve for x & y: Use the first equation to solve for y.

  4. Solve for y Add –2x to both sides of the equation. 2x – y = 10 -2x -2x -y = -2x + 10 Mentally multiply or divide by -1. -1(-y = -2x + 10) y = 2x - 10

  5. 4x – 3y = 16 (second equation) Substitute y = 2x -10 for y in the 2nd equation. 4x – 3(2x -10) = 16 Distribute. 4x - 6x + 30 = 16 -2x + 30 = 16 Subtract 30 on both sides. -2x + 30 = 16 -30 -30 -2x = -14 x = 7

  6. Ex. 59.3 Use substitution to solve for x & y:

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