Question

solve the system of equations.
$y = 14x + 5$
$y = 5x^{2} + 14x - 15$
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 \( y \), set \( 14x + 5 = 5x^2 + 14x - 15 \).

Step2: Simplify the equation

Subtract \( 14x + 5 \) from both sides: \( 0 = 5x^2 - 20 \).

Step3: Solve for \( x \)

Divide by 5: \( x^2 - 4 = 0 \), factor: \( (x - 2)(x + 2) = 0 \), so \( x = 2 \) or \( x = -2 \).

Step4: Find corresponding \( y \) values

For \( x = 2 \), \( y = 14(2) + 5 = 33 \).
For \( x = -2 \), \( y = 14(-2) + 5 = -23 \).

Answer:

\((2, 33)\)
\((-2, -23)\)