Question

solve the system of equations.
$y = -36x + 48$
$y = 5x^2 - 36x + 3$
write the coordinates in exact form. simplify all fractions and radicals.
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Explanation:

Step1: Set the two equations equal to each other

Since both equations are equal to \( y \), we can set them equal:
\( -36x + 48 = 5x^2 - 36x + 3 \)

Step2: Simplify the equation

Add \( 36x \) to both sides:
\( 48 = 5x^2 + 3 \)
Subtract 3 from both sides:
\( 5x^2 = 45 \)
Divide both sides by 5:
\( x^2 = 9 \)

Step3: Solve for \( x \)

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

Step4: Find the corresponding \( y \) values

For \( x = 3 \):
Substitute \( x = 3 \) into \( y = -36x + 48 \)
\( y = -36(3) + 48 = -108 + 48 = -60 \)
For \( x = -3 \):
Substitute \( x = -3 \) into \( y = -36x + 48 \)
\( y = -36(-3) + 48 = 108 + 48 = 156 \)

Answer:

\( (3, -60) \)
\( (-3, 156) \)