# ba co2

To balance the equation Ba + Co2 = BaCo3 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.

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

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

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a Ba + b Co2 = c BaCo3

### Step 2: Create a System of Equations

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

```Ba:	1a	+	0b	=	1c
Co:	0a	+	2b	=	3c

```

### Step 3: Solve For All Variables

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

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

```[ 1	 0	-1	0]
[ 0	 2	-3	0]
```

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

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

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• a = 2 (Ba)
• b = 3 (Co2)
• c = 2 (BaCo3)

### 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.

2 Ba + 3 Co2 = 2 BaCo3

Reactants Products Ba 2 2 ✔️ 6 6 ✔️

Since there is an equal number of each element in the reactants and products of 2Ba + 3Co2 = 2BaCo3, the equation is balanced.