Solve the system of equations.

y=

22x–17
y=3x2–22x–44
Write the coordinates in exact form. Simplify all fractions and radicals.
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1 answer

To solve the system of equations:

  1. \( y = -22x - 17 \)
  2. \( y = 3x^2 - 22x - 44 \)

we will set the two equations equal to each other since both are equal to \( y \):

\[ -22x - 17 = 3x^2 - 22x - 44 \]

Next, we can simplify this equation by adding \( 22x \) to both sides:

\[ -17 = 3x^2 - 44 \]

Now, we isolate the quadratic term:

\[ 3x^2 - 44 + 17 = 0 \] \[ 3x^2 - 27 = 0 \]

Next, we can add \( 27 \) to both sides:

\[ 3x^2 = 27 \]

Now, divide both sides by \( 3 \):

\[ x^2 = 9 \]

Taking the square root of both sides gives us:

\[ x = 3 \quad \text{or} \quad x = -3 \]

Now, let's find the corresponding \( y \) values for each \( x \):

  1. For \( x = 3 \):

\[ y = -22(3) - 17 = -66 - 17 = -83 \]

So, one solution is \( (3, -83) \).

  1. For \( x = -3 \):

\[ y = -22(-3) - 17 = 66 - 17 = 49 \]

So, the other solution is \( (-3, 49) \).

Putting it all together, the solutions to the system of equations are:

\[ (3, -83) \quad \text{and} \quad (-3, 49) \]