Question

solve the system of equations.
y = -15x - 4
y = 5x² - 15x - 49
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 equal \( y \), we set them equal to each other:
\( -15x - 4 = 5x^2 - 15x - 49 \)

Step2: Simplify the equation

Add \( 15x \) to both sides:
\( - 4 = 5x^2 - 49 \)
Add 49 to 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 into \( y = -15x - 4 \)
\( y = -15(3) - 4 = -45 - 4 = -49 \)

For \( x = -3 \):
Substitute into \( y = -15x - 4 \)
\( y = -15(-3) - 4 = 45 - 4 = 41 \)

Answer:

\( (3, -49) \)
\( (-3, 41) \)