Finite Math Examples

$x + y = 0$ , $x - y = 2$ , $- x + 4 y = 4$ , $x + y = 8$

Step 1

Subtract $y$ from both sides of the equation.

$x = - y$

$x - y = 2$

$- x + 4 y = 4$

$x + y = 8$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $x - y = 2$ with $- y$ .

$(- y) - y = 2$

$x = - y$

$- x + 4 y = 4$

$x + y = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $y$ from $- y$ .

$- 2 y = 2$

$x = - y$

$- x + 4 y = 4$

$x + y = 8$

$- 2 y = 2$

$x = - y$

$- x + 4 y = 4$

$x + y = 8$

Step 2.3

Replace all occurrences of $x$ in $- x + 4 y = 4$ with $- y$ .

$- (- y) + 4 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- (- y) + 4 y$ .

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Step 2.4.1.1

Multiply $- (- y)$ .

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Step 2.4.1.1.1

Multiply $- 1$ by $- 1$ .

$1 y + 4 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

Step 2.4.1.1.2

Multiply $y$ by $1$ .

$y + 4 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

$y + 4 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

Step 2.4.1.2

Add $y$ and $4 y$ .

$5 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

$x + y = 8$

Step 2.5

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

$(- y) + y = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

Step 2.6

Simplify the left side.

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Step 2.6.1

Add $- y$ and $y$ .

$0 = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

$0 = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

$0 = 8$

$5 y = 4$

$- 2 y = 2$

$x = - y$

Step 3

Since $0 = 8$ is not true, there is no solution.

No solution

Step 4