Precalculus Examples

$x + y + c = 1200$ , $4 x + 5 y + 6 c = 5300$

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the equation.

$y + c = 1200 - x$

$4 x + 5 y + 6 c = 5300$

Step 1.2

Subtract $c$ from both sides of the equation.

$y = 1200 - x - c$

$4 x + 5 y + 6 c = 5300$

$y = 1200 - x - c$

$4 x + 5 y + 6 c = 5300$

Step 2

Solve the equation for $c$ .

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Step 2.1

Simplify $4 x + 5 (1200 - x - c) + 6 c$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$4 x + 5 \cdot 1200 + 5 (- x) + 5 (- c) + 6 c = 5300$

$y = 1200 - x - c$

Step 2.1.1.2

Simplify.

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Step 2.1.1.2.1

Multiply $5$ by $1200$ .

$4 x + 6000 + 5 (- x) + 5 (- c) + 6 c = 5300$

$y = 1200 - x - c$

Step 2.1.1.2.2

Multiply $- 1$ by $5$ .

$4 x + 6000 - 5 x + 5 (- c) + 6 c = 5300$

$y = 1200 - x - c$

Step 2.1.1.2.3

Multiply $- 1$ by $5$ .

$4 x + 6000 - 5 x - 5 c + 6 c = 5300$

$y = 1200 - x - c$

$4 x + 6000 - 5 x - 5 c + 6 c = 5300$

$y = 1200 - x - c$

$4 x + 6000 - 5 x - 5 c + 6 c = 5300$

$y = 1200 - x - c$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Subtract $5 x$ from $4 x$ .

$- x + 6000 - 5 c + 6 c = 5300$

$y = 1200 - x - c$

Step 2.1.2.2

Add $- 5 c$ and $6 c$ .

$- x + 6000 + c = 5300$

$y = 1200 - x - c$

$- x + 6000 + c = 5300$

$y = 1200 - x - c$

$- x + 6000 + c = 5300$

$y = 1200 - x - c$

Step 2.2

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

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Step 2.2.1

Add $x$ to both sides of the equation.

$6000 + c = 5300 + x$

$y = 1200 - x - c$

Step 2.2.2

Subtract $6000$ from both sides of the equation.

$c = 5300 + x - 6000$

$y = 1200 - x - c$

Step 2.2.3

Subtract $6000$ from $5300$ .

$c = x - 700$

$y = 1200 - x - c$

$c = x - 700$

$y = 1200 - x - c$

$c = x - 700$

$y = 1200 - x - c$

Step 3

Simplify the right side.

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Step 3.1

Simplify $1200 - x - (x - 700)$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$y = 1200 - x - x + 700$

$c = x - 700$

Step 3.1.1.2

Multiply $- 1$ by $- 700$ .

$y = 1200 - x - x + 700$

$c = x - 700$

$y = 1200 - x - x + 700$

$c = x - 700$

Step 3.1.2

Simplify by adding terms.

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Step 3.1.2.1

Add $1200$ and $700$ .

$y = - x - x + 1900$

$c = x - 700$

Step 3.1.2.2

Subtract $x$ from $- x$ .

$y = - 2 x + 1900$

$c = x - 700$

$y = - 2 x + 1900$

$c = x - 700$

$y = - 2 x + 1900$

$c = x - 700$

$y = - 2 x + 1900$

$c = x - 700$

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