Finite Math Examples

$y + 3 x = 4$ , $6 x - 8 = - 2 y$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = 4 - 3 x$

$6 x - 8 = - 2 y$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $6 x - 8 = - 2 y$ with $4 - 3 x$ .

$6 x - 8 = - 2 (4 - 3 x)$

$y = 4 - 3 x$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 2 (4 - 3 x)$ .

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Step 2.2.1.1

Apply the distributive property.

$6 x - 8 = - 2 \cdot 4 - 2 (- 3 x)$

$y = 4 - 3 x$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $- 2$ by $4$ .

$6 x - 8 = - 8 - 2 (- 3 x)$

$y = 4 - 3 x$

Step 2.2.1.2.2

Multiply $- 3$ by $- 2$ .

$6 x - 8 = - 8 + 6 x$

$y = 4 - 3 x$

$6 x - 8 = - 8 + 6 x$

$y = 4 - 3 x$

$6 x - 8 = - 8 + 6 x$

$y = 4 - 3 x$

$6 x - 8 = - 8 + 6 x$

$y = 4 - 3 x$

$6 x - 8 = - 8 + 6 x$

$y = 4 - 3 x$

Step 3

Solve for $x$ in $6 x - 8 = - 8 + 6 x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $6 x$ from both sides of the equation.

$6 x - 8 - 6 x = - 8$

$y = 4 - 3 x$

Step 3.1.2

Combine the opposite terms in $6 x - 8 - 6 x$ .

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Step 3.1.2.1

Subtract $6 x$ from $6 x$ .

$0 - 8 = - 8$

$y = 4 - 3 x$

Step 3.1.2.2

Subtract $8$ from $0$ .

$- 8 = - 8$

$y = 4 - 3 x$

$- 8 = - 8$

$y = 4 - 3 x$

$- 8 = - 8$

$y = 4 - 3 x$

Step 3.2

Since $- 8 = - 8$ , the equation will always be true.

Always true

$y = 4 - 3 x$

Always true

$y = 4 - 3 x$

Step 4

Remove any equations from the system that are always true.

$y = 4 - 3 x$

Step 5