Finite Math Examples

$5 x - 6 x = - 7$ , $- 15 x + 18 x = 21$

Step 1

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

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Step 1.1

Subtract $6 x$ from $5 x$ .

$- x = - 7$

$- 15 x + 18 x = 21$

Step 1.2

Add $- 15 x$ and $18 x$ .

$- x = - 7$

$3 x = 21$

$- x = - 7$

$3 x = 21$

Step 2

Write the system as a matrix.

$[\begin{array}{c} - 1 & - 7 \\ 3 & 21 \end{array}]$

Step 3

Find the reduced row echelon form.

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Step 3.1

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

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Step 3.1.1

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

$[\begin{array}{c} - - 1 & - - 7 \\ 3 & 21 \end{array}]$

Step 3.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 7 \\ 3 & 21 \end{array}]$

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 $0$ .

$[\begin{array}{c} 1 & 7 \\ 3 - 3 \cdot 1 & 21 - 3 \cdot 7 \end{array}]$

Step 3.2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 7 \\ 0 & 0 \end{array}]$

Step 4

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

$x = 7$

$0 = 0$

Step 5

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

$(error = error)$