Solve the System of Equations y=2x^2-20x+13 2x+y=13

$y = 2 x^{2} - 20 x + 13$ $2 x + y = 13$

Replace all occurrences of $y$ with $2 x^{2} - 20 x + 13$ in each equation.

Replace all occurrences of $y$ in $2 x + y = 13$ with $2 x^{2} - 20 x + 13$ .

$2 x + 2 x^{2} - 20 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

Simplify the left side.

Simplify $2 x + 2 x^{2} - 20 x + 13$ .

Remove parentheses.

$2 x + 2 x^{2} - 20 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

Subtract $20 x$ from $2 x$ .

$2 x^{2} - 18 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

$2 x^{2} - 18 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

$2 x^{2} - 18 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

$2 x^{2} - 18 x + 13 = 13$

$y = 2 x^{2} - 20 x + 13$

Solve for $x$ in $2 x^{2} - 18 x + 13 = 13$ .

Subtract $13$ from both sides of the equation.

$2 x^{2} - 18 x + 13 - 13 = 0$

$y = 2 x^{2} - 20 x + 13$

Combine the opposite terms in $2 x^{2} - 18 x + 13 - 13$ .

Subtract $13$ from $13$ .

$2 x^{2} - 18 x + 0 = 0$

$y = 2 x^{2} - 20 x + 13$

Add $2 x^{2} - 18 x$ and $0$ .

$2 x^{2} - 18 x = 0$

$y = 2 x^{2} - 20 x + 13$

$2 x^{2} - 18 x = 0$

$y = 2 x^{2} - 20 x + 13$

Factor $2 x$ out of $2 x^{2} - 18 x$ .

Factor $2 x$ out of $2 x^{2}$ .

$2 x (x) - 18 x = 0$

$y = 2 x^{2} - 20 x + 13$

Factor $2 x$ out of $- 18 x$ .

$2 x (x) + 2 x (- 9) = 0$

$y = 2 x^{2} - 20 x + 13$

Factor $2 x$ out of $2 x (x) + 2 x (- 9)$ .

$2 x (x - 9) = 0$

$y = 2 x^{2} - 20 x + 13$

$2 x (x - 9) = 0$

$y = 2 x^{2} - 20 x + 13$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 9 = 0$

$y = 2 x^{2} - 20 x + 13$

Set $x$ equal to $0$ .

$x = 0$

$y = 2 x^{2} - 20 x + 13$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

$y = 2 x^{2} - 20 x + 13$

Add $9$ to both sides of the equation.

$x = 9$

$y = 2 x^{2} - 20 x + 13$

$x = 9$

$y = 2 x^{2} - 20 x + 13$

The final solution is all the values that make $2 x (x - 9) = 0$ true.

$x = 0, 9$

$y = 2 x^{2} - 20 x + 13$

$x = 0, 9$

$y = 2 x^{2} - 20 x + 13$

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

Replace all occurrences of $x$ in $y = 2 x^{2} - 20 x + 13$ with $0$ .

$y = 2 {(0)}^{2} - 20 \cdot 0 + 13$

$x = 0$

Simplify the right side.

Simplify $2 {(0)}^{2} - 20 \cdot 0 + 13$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = 2 \cdot 0 - 20 \cdot 0 + 13$

$x = 0$

Multiply $2$ by $0$ .

$y = 0 - 20 \cdot 0 + 13$

$x = 0$

Multiply $- 20$ by $0$ .

$y = 0 + 0 + 13$

$x = 0$

$y = 0 + 0 + 13$

$x = 0$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 13$

$x = 0$

Add $0$ and $13$ .

$y = 13$

$x = 0$

$y = 13$

$x = 0$

$y = 13$

$x = 0$

$y = 13$

$x = 0$

$y = 13$

$x = 0$

Replace all occurrences of $x$ with $9$ in each equation.

Replace all occurrences of $x$ in $y = 2 x^{2} - 20 x + 13$ with $9$ .

$y = 2 {(9)}^{2} - 20 \cdot 9 + 13$

$x = 9$

Simplify the right side.

Simplify $2 {(9)}^{2} - 20 \cdot 9 + 13$ .

Simplify each term.

Raise $9$ to the power of $2$ .

$y = 2 \cdot 81 - 20 \cdot 9 + 13$

$x = 9$

Multiply $2$ by $81$ .

$y = 162 - 20 \cdot 9 + 13$

$x = 9$

Multiply $- 20$ by $9$ .

$y = 162 - 180 + 13$

$x = 9$

$y = 162 - 180 + 13$

$x = 9$

Simplify by adding and subtracting.

Subtract $180$ from $162$ .

$y = - 18 + 13$

$x = 9$

Add $- 18$ and $13$ .

$y = - 5$

$x = 9$

$y = - 5$

$x = 9$

$y = - 5$

$x = 9$

$y = - 5$

$x = 9$

$y = - 5$

$x = 9$

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

$(0, 13)$

$(9, - 5)$

The result can be shown in multiple forms.

Point Form:

$(0, 13), (9, - 5)$

Equation Form:

$x = 0, y = 13$

$x = 9, y = - 5$

Solve the System of Equations y=2x^2-20x+13 2x+y=13

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