Finite Math Examples

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

Solve for $x$ in the first equation.

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Subtract $y$ from both sides of the equation.

$2 x = - 2 - y$

$x + 2 y = 2$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = - 2 - y$ by $2$ .

$\frac{2 x}{2} = - \frac{2}{2} - \frac{y}{2}$

$x + 2 y = 2$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{2 x}{2} = - \frac{2}{2} - \frac{y}{2}$

$x + 2 y = 2$

Divide $x$ by $1$ .

$x = - \frac{2}{2} - \frac{y}{2}$

$x + 2 y = 2$

$x = - \frac{2}{2} - \frac{y}{2}$

$x + 2 y = 2$

Simplify each term.

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Divide $2$ by $2$ .

$x = - 1 \cdot 1 - \frac{y}{2}$

$x + 2 y = 2$

Multiply $- 1$ by $1$ .

$x = - 1 - \frac{y}{2}$

$x + 2 y = 2$

$x = - 1 - \frac{y}{2}$

$x + 2 y = 2$

$x = - 1 - \frac{y}{2}$

$x + 2 y = 2$

$x = - 1 - \frac{y}{2}$

$x + 2 y = 2$

Replace all occurrences of $x$ with the solution found by solving the last equation for $x$ . In this case, the value substituted is $- 1 - \frac{y}{2}$ .

$x = - 1 - \frac{y}{2}$

$(- 1 - \frac{y}{2}) + 2 y = 2$

Solve for $y$ in the second equation.

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Simplify the left side.

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To write $\frac{2 y}{1}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - 1 - \frac{y}{2}$

$- 1 + (- \frac{y}{2} + \frac{2 y}{1} \cdot \frac{2}{2}) = 2$

Write each expression with a common denominator of $2$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$x = - 1 - \frac{y}{2}$

$- 1 + (- \frac{y}{2} + \frac{2 y \cdot 2}{1 \cdot 2}) = 2$

Multiply $2$ by $1$ .

$x = - 1 - \frac{y}{2}$

$- 1 + (- \frac{y}{2} + \frac{2 y \cdot 2}{2}) = 2$

$x = - 1 - \frac{y}{2}$

$- 1 + (- \frac{y}{2} + \frac{2 y \cdot 2}{2}) = 2$

Combine the numerators over the common denominator.

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{- y + 2 y \cdot 2}{2} = 2$

Simplify each term.

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Simplify the numerator.

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Factor $y$ out of $- y + 2 y \cdot 2$ .

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Factor $y$ out of $- y$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y \cdot - 1 + 2 y \cdot 2}{2} = 2$

Factor $y$ out of $2 y \cdot 2$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y \cdot - 1 + y (2 \cdot 2)}{2} = 2$

Factor $y$ out of $y \cdot - 1 + y (2 \cdot 2)$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y \cdot (- 1 + 2 \cdot 2)}{2} = 2$

Multiply $y$ by $- 1 + 2 \cdot 2$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y (- 1 + 2 \cdot 2)}{2} = 2$

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y (- 1 + 2 \cdot 2)}{2} = 2$

Multiply $2$ by $2$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y (- 1 + 4)}{2} = 2$

Add $- 1$ and $4$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y \cdot 3}{2} = 2$

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{y \cdot 3}{2} = 2$

Move $3$ to the left of the expression $y \cdot 3$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{3 \cdot y}{2} = 2$

Multiply $3$ by $y$ .

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{3 y}{2} = 2$

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{3 y}{2} = 2$

$x = - 1 - \frac{y}{2}$

$- 1 + \frac{3 y}{2} = 2$

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

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Add $1$ to both sides of the equation.

$x = - 1 - \frac{y}{2}$

$\frac{3 y}{2} = 2 + 1$

Add $2$ and $1$ .

$x = - 1 - \frac{y}{2}$

$\frac{3 y}{2} = 3$

$x = - 1 - \frac{y}{2}$

$\frac{3 y}{2} = 3$

Solve for $y$ .

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Multiply both sides of the equation by $2$ .

$x = - 1 - \frac{y}{2}$

$3 y = 3 \cdot (2)$

Simplify $3 \cdot (2)$ .

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Multiply $3$ by $2$ .

$x = - 1 - \frac{y}{2}$

$3 y = 3 (2)$

Multiply $3$ by $2$ .

$x = - 1 - \frac{y}{2}$

$3 y = 6$

$x = - 1 - \frac{y}{2}$

$3 y = 6$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 6$ by $3$ .

$x = - 1 - \frac{y}{2}$

$\frac{3 y}{3} = \frac{6}{3}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$x = - 1 - \frac{y}{2}$

$\frac{3 y}{3} = \frac{6}{3}$

Divide $y$ by $1$ .

$x = - 1 - \frac{y}{2}$

$y = \frac{6}{3}$

$x = - 1 - \frac{y}{2}$

$y = \frac{6}{3}$

Divide $6$ by $3$ .

$x = - 1 - \frac{y}{2}$

$y = 2$

$x = - 1 - \frac{y}{2}$

$y = 2$

$x = - 1 - \frac{y}{2}$

$y = 2$

$x = - 1 - \frac{y}{2}$

$y = 2$

Replace all occurrences of $y$ with the solution found by solving the last equation for $y$ . In this case, the value substituted is $2$ .

$x = - 1 - \frac{2}{2}$

$y = 2$

Simplify $- 1 - \frac{2}{2}$ .

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Simplify each term.

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Divide $2$ by $2$ .

$x = - 1 - 1 \cdot 1$

$y = 2$

Multiply $- 1$ by $1$ .

$x = - 1 - 1$

$y = 2$

$x = - 1 - 1$

$y = 2$

Subtract $1$ from $- 1$ .

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

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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