Finite Math Examples

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

Subtract $y$ from both sides of the equation.

$x = - y + 4$

$x - y = 2$

Replace all occurrences of $x$ with the solution found by solving the last equation for $x$ . In this case, the value substituted is $- y + 4$ .

$x = - y + 4$

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

Solve for $y$ in the second equation.

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Subtract $y$ from $- y$ .

$x = - y + 4$

$- 2 y + 4 = 2$

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

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Subtract $4$ from both sides of the equation.

$x = - y + 4$

$- 2 y = - 4 + 2$

Add $- 4$ and $2$ .

$x = - y + 4$

$- 2 y = - 2$

$x = - y + 4$

$- 2 y = - 2$

Divide each term by $- 2$ and simplify.

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

$x = - y + 4$

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

Simplify the left side of the $e q u a t i o n$ by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor $2$ out of $2 y$ .

$x = - y + 4$

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

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$x = - y + 4$

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

$x = - y + 4$

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

Simplify the expression.

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Multiply $- 1$ by $y$ .

$x = - y + 4$

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

Rewrite $- 1 y$ as $- y$ .

$x = - y + 4$

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

$x = - y + 4$

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

$x = - y + 4$

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

Divide $2$ by $- 2$ .

$x = - y + 4$

$y = 1$

$x = - y + 4$

$y = 1$

$x = - y + 4$

$y = 1$

Replace all occurrences of $y$ with the solution found by solving the last equation for $y$ . In this case, the value substituted is $1$ .

$x = - (1) + 4$

$y = 1$

Simplify the right side.

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Multiply $- 1$ by $1$ .

$x = - 1 + 4$

$y = 1$

Add $- 1$ and $4$ .

$x = 3$

$y = 1$

$x = 3$

$y = 1$

The solution can be shown in both point and equation forms.

Point Form:

$(3, 1)$

Equation Form: $x = 3 y = 1$

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