Finite Math Examples

$3 x + 5 y = - 3$ , $- 6 x - 10 y = 7$

Step 1

Solve for $x$ in $3 x + 5 y = - 3$ .

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Step 1.1

Subtract $5 y$ from both sides of the equation.

$3 x = - 3 - 5 y$

$- 6 x - 10 y = 7$

Step 1.2

Divide each term in $3 x = - 3 - 5 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = - 3 - 5 y$ by $3$ .

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

$- 6 x - 10 y = 7$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

$- 6 x - 10 y = 7$

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

$- 6 x - 10 y = 7$

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

$- 6 x - 10 y = 7$

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

$- 6 x - 10 y = 7$

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

Divide $- 3$ by $3$ .

$x = - 1 + \frac{- 5 y}{3}$

$- 6 x - 10 y = 7$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = - 1 - \frac{5 y}{3}$

$- 6 x - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$- 6 x - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$- 6 x - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$- 6 x - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$- 6 x - 10 y = 7$

Step 2

Replace all occurrences of $x$ with $- 1 - \frac{5 y}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 6 x - 10 y = 7$ with $- 1 - \frac{5 y}{3}$ .

$- 6 (- 1 - \frac{5 y}{3}) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 6 (- 1 - \frac{5 y}{3}) - 10 y$ .

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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.

$- 6 \cdot - 1 - 6 (- \frac{5 y}{3}) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.2

Multiply $- 6$ by $- 1$ .

$6 - 6 (- \frac{5 y}{3}) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{5 y}{3}$ into the numerator.

$6 - 6 \frac{- 5 y}{3} - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.3.2

Factor $3$ out of $- 6$ .

$6 + 3 (- 2) (\frac{- 5 y}{3}) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.3.3

Cancel the common factor.

$6 + 3 \cdot (- 2 \frac{- 5 y}{3}) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.3.4

Rewrite the expression.

$6 - 2 (- 5 y) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$6 - 2 (- 5 y) - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.1.4

Multiply $- 5$ by $- 2$ .

$6 + 10 y - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

$6 + 10 y - 10 y = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.2

Combine the opposite terms in $6 + 10 y - 10 y$ .

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Step 2.2.1.2.1

Subtract $10 y$ from $10 y$ .

$6 + 0 = 7$

$x = - 1 - \frac{5 y}{3}$

Step 2.2.1.2.2

Add $6$ and $0$ .

$6 = 7$

$x = - 1 - \frac{5 y}{3}$

$6 = 7$

$x = - 1 - \frac{5 y}{3}$

$6 = 7$

$x = - 1 - \frac{5 y}{3}$

$6 = 7$

$x = - 1 - \frac{5 y}{3}$

$6 = 7$

$x = - 1 - \frac{5 y}{3}$

Step 3

Since $6 = 7$ is not true, there is no solution.

No solution

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$