Solve by Substitution y=1/(x-3) , y=3-x^3

$y = \frac{1}{x - 3}$ , $y = 3 - x^{3}$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{1}{x - 3} = 3 - x^{3}$

Step 2

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

$x \approx 1.54490006 + y = 3 - x^{3}$

Step 3

Evaluate $y$ when $x = 1.54490006$ .

Substitute $1.54490006$ for $x$ .

$y = 3 - {(1.54490006)}^{3}$

Substitute $1.54490006$ for $x$ in $y = 3 - {(1.54490006)}^{3}$ and solve for $y$ .

Remove parentheses.

$y = 3 - {1.54490006}^{3}$

Remove parentheses.

$y = 3 - {(1.54490006)}^{3}$

Simplify $3 - {(1.54490006)}^{3}$ .

Simplify each term.

Raise $1.54490006$ to the power of $3$ .

$y = 3 - 1 \cdot 3.68723802$

Multiply $- 1$ by $3.68723802$ .

$y = 3 - 3.68723802$

Subtract $3.68723802$ from $3$ .

$y = - 0.68723802$

Step 4

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

$(1.54490006, - 0.68723802)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1.54490006, - 0.68723802)$

Equation Form:

$x = 1.54490006, y = - 0.68723802$

Step 6