Question: Use the ALEKS graphing calculator to solve the system of equations. \[ y = -3x - 17 \] \[ y =…

Use the ALEKS graphing calculator to solve the system of equations.

\[ y = -3x - 17 \]

\[ y = 2x^2 + 12x + 16 \]

Round to the nearest hundredth.

If there is more than one solution, use the “or” button.

If applicable, click on “No solution”.

\[ (x, y) = (\boxed{\phantom{00}}, \boxed{\phantom{00}}) \]

\[ \text{No solution} \]

Solution

To solve the system of equations, we’ll set the equations equal to each other and solve for \( x \). Given: \[ y = -3x - 17 \] \[ y = 2x^2 + 12x + 16 \] Set the equations equal: \[ -3x - 17 = 2x^2 + 12x + 16 \] Rearrange all terms to one side: \[ 0 = 2x^2 + 12x + 16 + 3x + 17 \] Simplify: \[ 0 = 2x^2 + 15x + 33 \] Use the quadratic formula to solve for \( x \): \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 2 \), \( b = 15 \), \( c = 33 \). Calculate the discriminant: \[ b^2 - 4ac = 15^2 - 4 \times 2 \times 33 \] \[ = 225 - 264 \] \[ = -39 \] Since the discriminant is negative, there are no real solutions. Thus, there is no solution to the system of equations.