Finite Math Examples

$x - y = 10$ , $- 8 x + 8 y = 3$

Step 1

Add $y$ to both sides of the equation.

$x = 10 + y$

$- 8 x + 8 y = 3$

Step 2

Replace all occurrences of $x$ with $10 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 8 x + 8 y = 3$ with $10 + y$ .

$- 8 (10 + y) + 8 y = 3$

$x = 10 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 8 (10 + y) + 8 y$ .

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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.

$- 8 \cdot 10 - 8 y + 8 y = 3$

$x = 10 + y$

Step 2.2.1.1.2

Multiply $- 8$ by $10$ .

$- 80 - 8 y + 8 y = 3$

$x = 10 + y$

$- 80 - 8 y + 8 y = 3$

$x = 10 + y$

Step 2.2.1.2

Combine the opposite terms in $- 80 - 8 y + 8 y$ .

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Step 2.2.1.2.1

Add $- 8 y$ and $8 y$ .

$- 80 + 0 = 3$

$x = 10 + y$

Step 2.2.1.2.2

Add $- 80$ and $0$ .

$- 80 = 3$

$x = 10 + y$

$- 80 = 3$

$x = 10 + y$

$- 80 = 3$

$x = 10 + y$

$- 80 = 3$

$x = 10 + y$

$- 80 = 3$

$x = 10 + y$

Step 3

Since $- 80 = 3$ is not true, there is no solution.

No solution

Step 4