Precalculus Examples

$25 x - 75 y = 100$ , $- 10 x + 30 y = - 40$

Step 1

Solve for $x$ in $25 x - 75 y = 100$ .

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Step 1.1

Add $75 y$ to both sides of the equation.

$25 x = 100 + 75 y$

$- 10 x + 30 y = - 40$

Step 1.2

Divide each term in $25 x = 100 + 75 y$ by $25$ and simplify.

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Step 1.2.1

Divide each term in $25 x = 100 + 75 y$ by $25$ .

$\frac{25 x}{25} = \frac{100}{25} + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $25$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{25 x}{25} = \frac{100}{25} + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{100}{25} + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

$x = \frac{100}{25} + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

$x = \frac{100}{25} + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

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 $100$ by $25$ .

$x = 4 + \frac{75 y}{25}$

$- 10 x + 30 y = - 40$

Step 1.2.3.1.2

Cancel the common factor of $75$ and $25$ .

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Step 1.2.3.1.2.1

Factor $25$ out of $75 y$ .

$x = 4 + \frac{25 (3 y)}{25}$

$- 10 x + 30 y = - 40$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $25$ out of $25$ .

$x = 4 + \frac{25 (3 y)}{25 (1)}$

$- 10 x + 30 y = - 40$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 4 + \frac{25 (3 y)}{25 \cdot 1}$

$- 10 x + 30 y = - 40$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 4 + \frac{3 y}{1}$

$- 10 x + 30 y = - 40$

Step 1.2.3.1.2.2.4

Divide $3 y$ by $1$ .

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

$x = 4 + 3 y$

$- 10 x + 30 y = - 40$

Step 2

Replace all occurrences of $x$ with $4 + 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 10 x + 30 y = - 40$ with $4 + 3 y$ .

$- 10 (4 + 3 y) + 30 y = - 40$

$x = 4 + 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 10 (4 + 3 y) + 30 y$ .

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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.

$- 10 \cdot 4 - 10 (3 y) + 30 y = - 40$

$x = 4 + 3 y$

Step 2.2.1.1.2

Multiply $- 10$ by $4$ .

$- 40 - 10 (3 y) + 30 y = - 40$

$x = 4 + 3 y$

Step 2.2.1.1.3

Multiply $3$ by $- 10$ .

$- 40 - 30 y + 30 y = - 40$

$x = 4 + 3 y$

$- 40 - 30 y + 30 y = - 40$

$x = 4 + 3 y$

Step 2.2.1.2

Combine the opposite terms in $- 40 - 30 y + 30 y$ .

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Step 2.2.1.2.1

Add $- 30 y$ and $30 y$ .

$- 40 + 0 = - 40$

$x = 4 + 3 y$

Step 2.2.1.2.2

Add $- 40$ and $0$ .

$- 40 = - 40$

$x = 4 + 3 y$

$- 40 = - 40$

$x = 4 + 3 y$

$- 40 = - 40$

$x = 4 + 3 y$

$- 40 = - 40$

$x = 4 + 3 y$

$- 40 = - 40$

$x = 4 + 3 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 + 3 y$

Step 4