Question

solve the system of equations.
( y = -29x + 72 )
( y = x^2 - 29x - 49 )
write the coordinates in exact form. simplify all fractions and radicals.
( (square, square) )
( (square, square) )

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we set them equal: \( -29x + 72 = x^2 - 29x - 49 \)

Step2: Simplify the equation

Add \( 29x \) to both sides: \( 72 = x^2 - 49 \)
Then add 49 to both sides: \( x^2 = 72 + 49 = 121 \)

Step3: Solve for \( x \)

Take the square root of both sides: \( x = \pm\sqrt{121} = \pm 11 \)

Step4: Find the corresponding \( y \) values

For \( x = 11 \): \( y = -29(11) + 72 = -319 + 72 = -247 \)
For \( x = -11 \): \( y = -29(-11) + 72 = 319 + 72 = 391 \)

Answer:

\((11, -247)\), \((-11, 391)\)