Finite Math Examples

$5 x \cdot 1 - 2 x \cdot 2 = - 9$ , $- 10 x \cdot 1 + 4 x \cdot 2 = 18$

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 $5$ by $1$ .

$5 x - 2 x \cdot 2 = - 9$

$- 10 x \cdot 1 + 4 x \cdot 2 = 18$

Step 1.1.2

Multiply $2$ by $- 2$ .

$5 x - 4 x = - 9$

$- 10 x \cdot 1 + 4 x \cdot 2 = 18$

$5 x - 4 x = - 9$

$- 10 x \cdot 1 + 4 x \cdot 2 = 18$

Step 1.2

Subtract $4 x$ from $5 x$ .

$x = - 9$

$- 10 x \cdot 1 + 4 x \cdot 2 = 18$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $- 10$ by $1$ .

$x = - 9$

$- 10 x + 4 x \cdot 2 = 18$

Step 1.3.2

Multiply $2$ by $4$ .

$x = - 9$

$- 10 x + 8 x = 18$

$x = - 9$

$- 10 x + 8 x = 18$

Step 1.4

Add $- 10 x$ and $8 x$ .

$x = - 9$

$- 2 x = 18$

$x = - 9$

$- 2 x = 18$

Step 2

Write the system as a matrix.

$[\begin{array}{c} 1 & - 9 \\ - 2 & 18 \end{array}]$

Step 3

Find the reduced row echelon form.

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Step 3.1

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

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Step 3.1.1

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

$[\begin{array}{c} 1 & - 9 \\ - 2 + 2 \cdot 1 & 18 + 2 \cdot - 9 \end{array}]$

Step 3.1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - 9 \\ 0 & 0 \end{array}]$

Step 4

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

$x = - 9$

$0 = 0$

Step 5

The solution is the set of ordered pairs that make the system true.

$(error = error)$