Finite Math Examples

$4 x + y = 5$ , $- 8 x - 2 y = 21$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 5 - 4 x$

$- 8 x - 2 y = 21$

Step 2

Replace all occurrences of $y$ with $5 - 4 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 8 x - 2 y = 21$ with $5 - 4 x$ .

$- 8 x - 2 (5 - 4 x) = 21$

$y = 5 - 4 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 8 x - 2 (5 - 4 x)$ .

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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.

$- 8 x - 2 \cdot 5 - 2 (- 4 x) = 21$

$y = 5 - 4 x$

Step 2.2.1.1.2

Multiply $- 2$ by $5$ .

$- 8 x - 10 - 2 (- 4 x) = 21$

$y = 5 - 4 x$

Step 2.2.1.1.3

Multiply $- 4$ by $- 2$ .

$- 8 x - 10 + 8 x = 21$

$y = 5 - 4 x$

$- 8 x - 10 + 8 x = 21$

$y = 5 - 4 x$

Step 2.2.1.2

Combine the opposite terms in $- 8 x - 10 + 8 x$ .

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Step 2.2.1.2.1

Add $- 8 x$ and $8 x$ .

$0 - 10 = 21$

$y = 5 - 4 x$

Step 2.2.1.2.2

Subtract $10$ from $0$ .

$- 10 = 21$

$y = 5 - 4 x$

$- 10 = 21$

$y = 5 - 4 x$

$- 10 = 21$

$y = 5 - 4 x$

$- 10 = 21$

$y = 5 - 4 x$

$- 10 = 21$

$y = 5 - 4 x$

Step 3

Since $- 10 = 21$ is not true, there is no solution.

No solution

Step 4