Finite Math Examples

$2 x + y = - 2$ , $x + 2 y = 2$

Subtract $2 x$ from both sides of the equation.

$y = - 2 - 2 x$

$x + 2 y = 2$

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

$y = - 2 - 2 x$

$x + 2 (- 2 - 2 x) = 2$

Simplify $x + 2 (- 2 - 2 x)$ .

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Simplify each term.

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Apply the distributive property.

$y = - 2 - 2 x$

$x + 2 \cdot - 2 + 2 (- 2 x) = 2$

Multiply $2$ by $- 2$ .

$y = - 2 - 2 x$

$x - 4 + 2 (- 2 x) = 2$

Multiply $- 2$ by $2$ .

$y = - 2 - 2 x$

$x - 4 - 4 x = 2$

$y = - 2 - 2 x$

$x - 4 - 4 x = 2$

Subtract $4 x$ from $x$ .

$y = - 2 - 2 x$

$- 3 x - 4 = 2$

$y = - 2 - 2 x$

$- 3 x - 4 = 2$

Solve for $x$ in the second equation.

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Move all terms not containing $x$ to the right side of the equation.

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Add $4$ to both sides of the equation.

$y = - 2 - 2 x$

$- 3 x = 2 + 4$

Add $2$ and $4$ .

$y = - 2 - 2 x$

$- 3 x = 6$

$y = - 2 - 2 x$

$- 3 x = 6$

Divide each term by $- 3$ and simplify.

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Divide each term in $- 3 x = 6$ by $- 3$ .

$y = - 2 - 2 x$

$\frac{- 3 x}{- 3} = \frac{6}{- 3}$

Cancel the common factor of $- 3$ .

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Cancel the common factor.

$y = - 2 - 2 x$

$\frac{- 3 x}{- 3} = \frac{6}{- 3}$

Divide $x$ by $1$ .

$y = - 2 - 2 x$

$x = \frac{6}{- 3}$

$y = - 2 - 2 x$

$x = \frac{6}{- 3}$

Divide $6$ by $- 3$ .

$y = - 2 - 2 x$

$x = - 2$

$y = - 2 - 2 x$

$x = - 2$

$y = - 2 - 2 x$

$x = - 2$

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

$y = - 2 - 2 \cdot - 2$

$x = - 2$

Simplify $- 2 - 2 \cdot - 2$ .

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Multiply $- 2$ by $- 2$ .

$y = - 2 + 4$

$x = - 2$

Add $- 2$ and $4$ .

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

The solution to the system of equations can be represented as a point.

$(- 2, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

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