Question

solve the system of equations.
$y = x^2 + 49x - 34$
$y = 49x + 30$
write the coordinates in exact form. simplify all fractions and radicals.
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Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( x^2 + 49x - 34 = 49x + 30 \).

Step2: Simplify the equation

Subtract \( 49x \) from both sides: \( x^2 - 34 = 30 \). Then add 34 to both sides: \( x^2 = 64 \).

Step3: Solve for \( x \)

Take square roots: \( x = \pm\sqrt{64} = \pm 8 \).

Step4: Find corresponding \( y \)

For \( x = 8 \): \( y = 49(8) + 30 = 392 + 30 = 422 \).
For \( x = -8 \): \( y = 49(-8) + 30 = -392 + 30 = -362 \).

Answer:

\((8, 422)\), \((-8, -362)\)