Finite Math Examples

$- 8 x - 3 y = 10$ , $16 x + 6 y = - 19$

Step 1

Solve for $x$ in $- 8 x - 3 y = 10$ .

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Step 1.1

Add $3 y$ to both sides of the equation.

$- 8 x = 10 + 3 y$

$16 x + 6 y = - 19$

Step 1.2

Divide each term in $- 8 x = 10 + 3 y$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 x = 10 + 3 y$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{10}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{10}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

$x = \frac{10}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

$x = \frac{10}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $10$ and $- 8$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{- 8} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $- 8$ .

$x = \frac{2 \cdot 5}{2 \cdot - 4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot - 4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{5}{- 4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

$x = \frac{5}{- 4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

$x = \frac{5}{- 4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = - \frac{5}{4} + \frac{3 y}{- 8}$

$16 x + 6 y = - 19$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = - \frac{5}{4} - \frac{3 y}{8}$

$16 x + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$16 x + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$16 x + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$16 x + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$16 x + 6 y = - 19$

Step 2

Replace all occurrences of $x$ with $- \frac{5}{4} - \frac{3 y}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $16 x + 6 y = - 19$ with $- \frac{5}{4} - \frac{3 y}{8}$ .

$16 (- \frac{5}{4} - \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $16 (- \frac{5}{4} - \frac{3 y}{8}) + 6 y$ .

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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.

$16 (- \frac{5}{4}) + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$16 (\frac{- 5}{4}) + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.2.2

Factor $4$ out of $16$ .

$4 (4) (\frac{- 5}{4}) + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.2.3

Cancel the common factor.

$4 \cdot (4 (\frac{- 5}{4})) + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.2.4

Rewrite the expression.

$4 \cdot - 5 + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$4 \cdot - 5 + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.3

Multiply $4$ by $- 5$ .

$- 20 + 16 (- \frac{3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.4

Cancel the common factor of $8$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{3 y}{8}$ into the numerator.

$- 20 + 16 (\frac{- 3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.4.2

Factor $8$ out of $16$ .

$- 20 + 8 (2) (\frac{- 3 y}{8}) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.4.3

Cancel the common factor.

$- 20 + 8 \cdot (2 (\frac{- 3 y}{8})) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.4.4

Rewrite the expression.

$- 20 + 2 (- 3 y) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 + 2 (- 3 y) + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.1.5

Multiply $- 3$ by $2$ .

$- 20 - 6 y + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 - 6 y + 6 y = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.2

Combine the opposite terms in $- 20 - 6 y + 6 y$ .

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Step 2.2.1.2.1

Add $- 6 y$ and $6 y$ .

$- 20 + 0 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 2.2.1.2.2

Add $- 20$ and $0$ .

$- 20 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

$- 20 = - 19$

$x = - \frac{5}{4} - \frac{3 y}{8}$

Step 3

Since $- 20 = - 19$ is not true, there is no solution.

No solution

Step 4