To balance the equation KClO3 + KCl = KClO using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

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### Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable to lớn represent the unknown coefficients.

a KClO_{3} + b KCl = c KClO

### Step 2: Create a System of Equations

Create an equation for each element (K, Cl, O) where each term represents the number of atoms of the element in each reactant or product.

**K**: 1a + 1b = 1c
**Cl**: 1a + 1b = 1c
**O**: 3a + 0b = 1c

### Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator to lớn solve for each variable.

- 1a + 1b - 1c = 0
- 1a + 1b - 1c = 0
- 3a - 1c = 0

Use your graphing calculator's rref() function (or an online rref calculator) to lớn convert the following matrix into reduced row-echelon-form:

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[ 1 1 -1 0] [ 1 1 -1 0] [ 3 0 -1 0]

The resulting matrix can be used to lớn determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result to lớn get the lowest, whole integer values.

- a = 1 (KClO3)
- b = 2 (KCl)
- c = 3 (KClO)

### Step 4: Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

KClO_{3} + 2 KCl = 3 KClO

K | 3 | 3 | ✔️ |
---|---|---|---|

Cl | 3 | 3 | ✔️ |

O | 3 | 3 | ✔️ |

Since there is an equal number of each element in the reactants and products of KClO3 + 2KCl = 3KClO, the equation is balanced.

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