Algebra Examples

$y = e^{x}$ , $x - y + 1 = 0$

Replace all occurrences of $y$ with $e^{x}$ in each equation.

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Replace all occurrences of $y$ in $x - y + 1 = 0$ with $e^{x}$ .

$x - (e^{x}) + 1 = 0$

$y = e^{x}$

Simplify the left side.

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Multiply $- 1$ by $e^{x}$ .

$x - e^{x} + 1 = 0$

$y = e^{x}$

$x - e^{x} + 1 = 0$

$y = e^{x}$

$x - e^{x} + 1 = 0$

$y = e^{x}$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 0$

$y = e^{x}$

Replace all occurrences of $x$ with $0$ in each equation.

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Replace all occurrences of $x$ in $y = e^{x}$ with $0$ .

$y = e^{0}$

$x = 0$

Simplify the right side.

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Anything raised to $0$ is $1$ .

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, 1)$

The result can be shown in multiple forms.

Point Form:

$(0, 1)$

Equation Form:

$x = 0, y = 1$