How to Solve a System of Two Linear Equations

Step-by-Step Guide

1. 1

   Step 1: Determine what the unknowns are and assign them variables.

   For example, let x = price of one apple, y = price of one orange.
2. 2

   Step 2: Set up the equations.

   For example:
   If 4 apples and 5 oranges cost $2, write 4x + 5y =
   2. (Eq. 1) If 3 apples and 4 oranges cost $1.55, write 3x + 4y =
   1.55. (Eq. 2) , Let's solve for x by eliminating y.
   
   The steps are Multiply Eq. 1 by the coefficient of the other variable (y) in Eq. 2 Multiplying Eq. 1 by 4, we get 16x + 20y = 8 Multiply Eq. 2 by the coefficient of the other variable (y) in Eq. 1 Multiplying Eq. 2 by 5 we get 15x + 20y =
   7.75 Subtract the two equations We get x =
   0.25.
   
   Therefore, price of an apple in the example is $0.25 To find the value of the other variable (y), plug in the value of x obtained in any of the equations we had.
   
   Plugging in x =
   0.25 in Eq. 1 we get, 4(0.25) + 5y = 2 => 1 + 5y = 2 => 5y = 2
   - 1 => 5y = 1 => y = 1/5 =
   0.20 Therefore, price of an orange in the example is $0.20 By the Method of Substitution Read on the LifeGuide Hub How to Solve Simultaneous Equations Using Substitution Method
3. 3

   Step 3: Solve By the Method of Elimination In this method we first solve for a variable by eliminating the other variable.

Detailed Guide

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