Question

solve the system of equations.
\\( y = 15x - 10 \\)
\\( y = 7x^2 + 15x - 38 \\)
write the coordinates in exact form. simplify all fractions and radicals.
( , )
( , )

Explanation:

Step1: Set the two equations equal

Since both equations are equal to \( y \), we can set them equal to each other:
\( 15x - 10 = 7x^2 + 15x - 38 \)

Step2: Simplify the equation

Subtract \( 15x \) from both sides:
\( -10 = 7x^2 - 38 \)

Add 38 to both sides:
\( 7x^2 = 28 \)

Divide both sides by 7:
\( x^2 = 4 \)

Take the square root of both sides:
\( x = \pm 2 \)

Step3: Find the corresponding \( y \)-values

For \( x = 2 \):
Substitute \( x = 2 \) into \( y = 15x - 10 \):
\( y = 15(2) - 10 = 30 - 10 = 20 \)

For \( x = -2 \):
Substitute \( x = -2 \) into \( y = 15x - 10 \):
\( y = 15(-2) - 10 = -30 - 10 = -40 \)

Answer:

\((2, 20)\)
\((-2, -40)\)