Finite Math Examples

$0.77 s \cdot 1 - 0.11 s \cdot 2 = 0$ , $s \cdot 1 + s \cdot 2 = 1$

Step 1

Move variables to the left and constant terms to the right.

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $0.77$ by $1$ .

$0.77 s - 0.11 s \cdot 2 = 0$

$s \cdot 1 + s \cdot 2 = 1$

Step 1.1.2

Multiply $2$ by $- 0.11$ .

$0.77 s - 0.22 s = 0$

$s \cdot 1 + s \cdot 2 = 1$

$0.77 s - 0.22 s = 0$

$s \cdot 1 + s \cdot 2 = 1$

Step 1.2

Subtract $0.22 s$ from $0.77 s$ .

$0.55 s = 0$

$s \cdot 1 + s \cdot 2 = 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $s$ by $1$ .

$0.55 s = 0$

$s + s \cdot 2 = 1$

Step 1.3.2

Move $2$ to the left of $s$ .

$0.55 s = 0$

$s + 2 s = 1$

$0.55 s = 0$

$s + 2 s = 1$

Step 1.4

Add $s$ and $2 s$ .

$0.55 s = 0$

$3 s = 1$

$0.55 s = 0$

$3 s = 1$

Step 2

Write the system as a matrix.

$[\begin{array}{c} 0.55 & 0 \\ 3 & 1 \end{array}]$

Step 3

Find the reduced row echelon form.

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Step 3.1

Multiply each element of $R_{1}$ by $\frac{1}{0.55}$ to make the entry at $1, 1$ a $1$ .

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Step 3.1.1

Multiply each element of $R_{1}$ by $\frac{1}{0.55}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{0.55}{0.55} & \frac{0}{0.55} \\ 3 & 1 \end{array}]$

Step 3.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 \\ 3 & 1 \end{array}]$

Step 3.2

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 3.2.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 \\ 3 - 3 \cdot 1 & 1 - 3 \cdot 0 \end{array}]$

Step 3.2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Step 4

Use the result matrix to declare the final solution to the system of equations.

$s = 0$

$0 = 1$

Step 5

The system is inconsistent so there is no solution.

$No solution$