Question

solve the system of equations.

$y = -36x + 1$

$y = 5x^2 - 36x - 44$

write the coordinates in exact form. simplify all fractions and radicals.

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Explanation:

Step1: Set the two equations equal

Since both equations are equal to \( y \), we can set them equal to each other:
\( -36x + 1 = 5x^2 - 36x - 44 \)

Step2: Simplify the equation

Add \( 36x \) to both sides:
\( 1 = 5x^2 - 44 \)

Step3: Solve for \( x^2 \)

Add 44 to both sides:
\( 5x^2 = 45 \)
Divide both sides by 5:
\( x^2 = 9 \)

Step4: Solve for \( x \)

Take the square root of both sides:
\( x = \pm 3 \)

Step5: Find the corresponding \( y \) values

For \( x = 3 \):
Substitute \( x = 3 \) into \( y = -36x + 1 \)
\( y = -36(3) + 1 = -108 + 1 = -107 \)

For \( x = -3 \):
Substitute \( x = -3 \) into \( y = -36x + 1 \)
\( y = -36(-3) + 1 = 108 + 1 = 109 \)

Answer:

\( (3, -107) \)
\( (-3, 109) \)