Solve the System of Equations y=x^2+2x-19 7y-14x=-21

$y = x^{2} + 2 x - 19$ $7 y - 14 x = - 21$

Replace all occurrences of $y$ with $x^{2} + 2 x - 19$ in each equation.

Replace all occurrences of $y$ in $7 y - 14 x = - 21$ with $x^{2} + 2 x - 19$ .

$7 (x^{2} + 2 x - 19) - 14 x = - 21$

$y = x^{2} + 2 x - 19$

Simplify the left side.

Simplify $7 (x^{2} + 2 x - 19) - 14 x$ .

Simplify each term.

Apply the distributive property.

$7 x^{2} + 7 (2 x) + 7 \cdot - 19 - 14 x = - 21$

$y = x^{2} + 2 x - 19$

Simplify.

Multiply $2$ by $7$ .

$7 x^{2} + 14 x + 7 \cdot - 19 - 14 x = - 21$

$y = x^{2} + 2 x - 19$

Multiply $7$ by $- 19$ .

$7 x^{2} + 14 x - 133 - 14 x = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} + 14 x - 133 - 14 x = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} + 14 x - 133 - 14 x = - 21$

$y = x^{2} + 2 x - 19$

Combine the opposite terms in $7 x^{2} + 14 x - 133 - 14 x$ .

Subtract $14 x$ from $14 x$ .

$7 x^{2} + 0 - 133 = - 21$

$y = x^{2} + 2 x - 19$

Add $7 x^{2}$ and $0$ .

$7 x^{2} - 133 = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} - 133 = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} - 133 = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} - 133 = - 21$

$y = x^{2} + 2 x - 19$

$7 x^{2} - 133 = - 21$

$y = x^{2} + 2 x - 19$

Solve for $x$ in $7 x^{2} - 133 = - 21$ .

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

Add $133$ to both sides of the equation.

$7 x^{2} = - 21 + 133$

$y = x^{2} + 2 x - 19$

Add $- 21$ and $133$ .

$7 x^{2} = 112$

$y = x^{2} + 2 x - 19$

$7 x^{2} = 112$

$y = x^{2} + 2 x - 19$

Divide each term in $7 x^{2} = 112$ by $7$ and simplify.

Divide each term in $7 x^{2} = 112$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{112}{7}$

$y = x^{2} + 2 x - 19$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{112}{7}$

$y = x^{2} + 2 x - 19$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{112}{7}$

$y = x^{2} + 2 x - 19$

$x^{2} = \frac{112}{7}$

$y = x^{2} + 2 x - 19$

$x^{2} = \frac{112}{7}$

$y = x^{2} + 2 x - 19$

Simplify the right side.

Divide $112$ by $7$ .

$x^{2} = 16$

$y = x^{2} + 2 x - 19$

$x^{2} = 16$

$y = x^{2} + 2 x - 19$

$x^{2} = 16$

$y = x^{2} + 2 x - 19$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{16}$

$y = x^{2} + 2 x - 19$

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

$y = x^{2} + 2 x - 19$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 4$

$y = x^{2} + 2 x - 19$

$x = \pm 4$

$y = x^{2} + 2 x - 19$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 4$

$y = x^{2} + 2 x - 19$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 4$

$y = x^{2} + 2 x - 19$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 4, - 4$

$y = x^{2} + 2 x - 19$

$x = 4, - 4$

$y = x^{2} + 2 x - 19$

$x = 4, - 4$

$y = x^{2} + 2 x - 19$

Replace all occurrences of $x$ with $4$ in each equation.

Replace all occurrences of $x$ in $y = x^{2} + 2 x - 19$ with $4$ .

$y = {(4)}^{2} + 2 (4) - 19$

$x = 4$

Simplify the right side.

Simplify ${(4)}^{2} + 2 (4) - 19$ .

Simplify each term.

Raise $4$ to the power of $2$ .

$y = 16 + 2 (4) - 19$

$x = 4$

Multiply $2$ by $4$ .

$y = 16 + 8 - 19$

$x = 4$

$y = 16 + 8 - 19$

$x = 4$

Simplify by adding and subtracting.

Add $16$ and $8$ .

$y = 24 - 19$

$x = 4$

Subtract $19$ from $24$ .

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

Replace all occurrences of $x$ with $- 4$ in each equation.

Replace all occurrences of $x$ in $y = x^{2} + 2 x - 19$ with $- 4$ .

$y = {(- 4)}^{2} + 2 (- 4) - 19$

$x = - 4$

Simplify the right side.

Simplify ${(- 4)}^{2} + 2 (- 4) - 19$ .

Simplify each term.

Raise $- 4$ to the power of $2$ .

$y = 16 + 2 (- 4) - 19$

$x = - 4$

Multiply $2$ by $- 4$ .

$y = 16 - 8 - 19$

$x = - 4$

$y = 16 - 8 - 19$

$x = - 4$

Simplify by subtracting numbers.

Subtract $8$ from $16$ .

$y = 8 - 19$

$x = - 4$

Subtract $19$ from $8$ .

$y = - 11$

$x = - 4$

$y = - 11$

$x = - 4$

$y = - 11$

$x = - 4$

$y = - 11$

$x = - 4$

$y = - 11$

$x = - 4$

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

$(4, 5)$

$(- 4, - 11)$

The result can be shown in multiple forms.

Point Form:

$(4, 5), (- 4, - 11)$

Equation Form:

$x = 4, y = 5$

$x = - 4, y = - 11$

Solve the System of Equations y=x^2+2x-19 7y-14x=-21

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