Finite Math Examples

$x + y = 1607$ , $x = 107 + y$

Step 1

Subtract $y$ from both sides of the equation.

$x = 1607 - y$

$x = 107 + y$

Step 2

Replace all occurrences of $x$ with $1607 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x = 1607 - y$ with $1607 - y$ .

$1607 - y = 1607 - y$

$x = 107 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Remove parentheses.

$1607 - y = 1607 - y$

$x = 107 + y$

$1607 - y = 1607 - y$

$x = 107 + y$

Step 2.3

Replace all occurrences of $x$ in $x = 107 + y$ with $1607 - y$ .

$1607 - y = 107 + y$

$1607 - y = 1607 - y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Remove parentheses.

$1607 - y = 107 + y$

$1607 - y = 1607 - y$

$1607 - y = 107 + y$

$1607 - y = 1607 - y$

$1607 - y = 107 + y$

$1607 - y = 1607 - y$

Step 3

Remove any equations from the system that are always true.

$1607 - y = 107 + y$

Step 4

Solve for $y$ in $1607 - y = 107 + y$ .

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Step 4.1

Move all terms containing $y$ to the left side of the equation.

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Step 4.1.1

Subtract $y$ from both sides of the equation.

$1607 - y - y = 107$

Step 4.1.2

Subtract $y$ from $- y$ .

$1607 - 2 y = 107$

Step 4.2

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

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Step 4.2.1

Subtract $1607$ from both sides of the equation.

$- 2 y = 107 - 1607$

Step 4.2.2

Subtract $1607$ from $107$ .

$- 2 y = - 1500$

Step 4.3

Divide each term in $- 2 y = - 1500$ by $- 2$ and simplify.

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Step 4.3.1

Divide each term in $- 2 y = - 1500$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 1500}{- 2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 1500}{- 2}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1500}{- 2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 1500$ by $- 2$ .

$y = 750$

Step 5