Finite Math Examples

$x + 4 y = 8$ , $7 x + 28 y = 56$

Step 1

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

$x = 8 - 4 y$

$7 x + 28 y = 56$

Step 2

Replace all occurrences of $x$ with $8 - 4 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $7 x + 28 y = 56$ with $8 - 4 y$ .

$7 (8 - 4 y) + 28 y = 56$

$x = 8 - 4 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $7 (8 - 4 y) + 28 y$ .

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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.

$7 \cdot 8 + 7 (- 4 y) + 28 y = 56$

$x = 8 - 4 y$

Step 2.2.1.1.2

Multiply $7$ by $8$ .

$56 + 7 (- 4 y) + 28 y = 56$

$x = 8 - 4 y$

Step 2.2.1.1.3

Multiply $- 4$ by $7$ .

$56 - 28 y + 28 y = 56$

$x = 8 - 4 y$

$56 - 28 y + 28 y = 56$

$x = 8 - 4 y$

Step 2.2.1.2

Combine the opposite terms in $56 - 28 y + 28 y$ .

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Step 2.2.1.2.1

Add $- 28 y$ and $28 y$ .

$56 + 0 = 56$

$x = 8 - 4 y$

Step 2.2.1.2.2

Add $56$ and $0$ .

$56 = 56$

$x = 8 - 4 y$

$56 = 56$

$x = 8 - 4 y$

$56 = 56$

$x = 8 - 4 y$

$56 = 56$

$x = 8 - 4 y$

$56 = 56$

$x = 8 - 4 y$

Step 3

Remove any equations from the system that are always true.

$x = 8 - 4 y$

Step 4