Finite Math Examples

$x + y + z = 10000$ , $y + 5 z = 27200$ , $z = 5200$

Step 1

Replace all occurrences of $z$ with $5200$ in each equation.

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Step 1.1

Replace all occurrences of $z$ in $x + y + z = 10000$ with $5200$ .

$x + y + 5200 = 10000$

$z = 5200$

$y + 5 z = 27200$

Step 1.2

Simplify the left side.

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Step 1.2.1

Remove parentheses.

$x + y + 5200 = 10000$

$z = 5200$

$y + 5 z = 27200$

$x + y + 5200 = 10000$

$z = 5200$

$y + 5 z = 27200$

Step 1.3

Replace all occurrences of $z$ in $y + 5 z = 27200$ with $5200$ .

$y + 5 (5200) = 27200$

$x + y + 5200 = 10000$

$z = 5200$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $5$ by $5200$ .

$y + 26000 = 27200$

$x + y + 5200 = 10000$

$z = 5200$

$y + 26000 = 27200$

$x + y + 5200 = 10000$

$z = 5200$

$y + 26000 = 27200$

$x + y + 5200 = 10000$

$z = 5200$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Subtract $26000$ from both sides of the equation.

$y = 27200 - 26000$

$x + y + 5200 = 10000$

$z = 5200$

Step 2.2

Subtract $26000$ from $27200$ .

$y = 1200$

$x + y + 5200 = 10000$

$z = 5200$

$y = 1200$

$x + y + 5200 = 10000$

$z = 5200$

Step 3

Replace all occurrences of $y$ with $1200$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x + y + 5200 = 10000$ with $1200$ .

$x + 1200 + 5200 = 10000$

$y = 1200$

$z = 5200$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $x + 1200 + 5200$ .

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Step 3.2.1.1

Remove parentheses.

$x + 1200 + 5200 = 10000$

$y = 1200$

$z = 5200$

Step 3.2.1.2

Add $1200$ and $5200$ .

$x + 6400 = 10000$

$y = 1200$

$z = 5200$

$x + 6400 = 10000$

$y = 1200$

$z = 5200$

$x + 6400 = 10000$

$y = 1200$

$z = 5200$

$x + 6400 = 10000$

$y = 1200$

$z = 5200$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Subtract $6400$ from both sides of the equation.

$x = 10000 - 6400$

$y = 1200$

$z = 5200$

Step 4.2

Subtract $6400$ from $10000$ .

$x = 3600$

$y = 1200$

$z = 5200$

$x = 3600$

$y = 1200$

$z = 5200$

Step 5

Solve the system of equations.

$x = 3600 y = 1200 z = 5200$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(3600, 1200, 5200)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3600, 1200, 5200)$

Equation Form:

$x = 3600, y = 1200, z = 5200$