Finite Math Examples

$7 x - y = 58$ , $x + 8 y = 49$

Step 1

Subtract $8 y$ from both sides of the equation.

$x = 49 - 8 y$

$7 x - y = 58$

Step 2

Replace all occurrences of $x$ with $49 - 8 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $7 x - y = 58$ with $49 - 8 y$ .

$7 (49 - 8 y) - y = 58$

$x = 49 - 8 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $7 (49 - 8 y) - y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$7 \cdot 49 + 7 (- 8 y) - y = 58$

$x = 49 - 8 y$

Step 2.2.1.1.2

Multiply $7$ by $49$ .

$343 + 7 (- 8 y) - y = 58$

$x = 49 - 8 y$

Step 2.2.1.1.3

Multiply $- 8$ by $7$ .

$343 - 56 y - y = 58$

$x = 49 - 8 y$

$343 - 56 y - y = 58$

$x = 49 - 8 y$

Step 2.2.1.2

Subtract $y$ from $- 56 y$ .

$343 - 57 y = 58$

$x = 49 - 8 y$

$343 - 57 y = 58$

$x = 49 - 8 y$

$343 - 57 y = 58$

$x = 49 - 8 y$

$343 - 57 y = 58$

$x = 49 - 8 y$

Step 3

Solve for $y$ in $343 - 57 y = 58$ .

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Step 3.1

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

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Step 3.1.1

Subtract $343$ from both sides of the equation.

$- 57 y = 58 - 343$

$x = 49 - 8 y$

Step 3.1.2

Subtract $343$ from $58$ .

$- 57 y = - 285$

$x = 49 - 8 y$

$- 57 y = - 285$

$x = 49 - 8 y$

Step 3.2

Divide each term in $- 57 y = - 285$ by $- 57$ and simplify.

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Step 3.2.1

Divide each term in $- 57 y = - 285$ by $- 57$ .

$\frac{- 57 y}{- 57} = \frac{- 285}{- 57}$

$x = 49 - 8 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 57$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 57 y}{- 57} = \frac{- 285}{- 57}$

$x = 49 - 8 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 285}{- 57}$

$x = 49 - 8 y$

$y = \frac{- 285}{- 57}$

$x = 49 - 8 y$

$y = \frac{- 285}{- 57}$

$x = 49 - 8 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 285$ by $- 57$ .

$y = 5$

$x = 49 - 8 y$

$y = 5$

$x = 49 - 8 y$

$y = 5$

$x = 49 - 8 y$

$y = 5$

$x = 49 - 8 y$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 49 - 8 y$ with $5$ .

$x = 49 - 8 \cdot 5$

$y = 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $49 - 8 \cdot 5$ .

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Step 4.2.1.1

Multiply $- 8$ by $5$ .

$x = 49 - 40$

$y = 5$

Step 4.2.1.2

Subtract $40$ from $49$ .

$x = 9$

$y = 5$

$x = 9$

$y = 5$

$x = 9$

$y = 5$

$x = 9$

$y = 5$

Step 5

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

$(9, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 5)$

Equation Form:

$x = 9, y = 5$

Step 7