Question

solve the following system of equations algebraically:
$y = 5x^2 + 26x$
$y = -3x + 6$
answer attempt 1 out of 2
two solutions
and

Explanation:

Step1: Set the two equations equal

Since both equal \( y \), we set \( 5x^2 + 26x = -3x + 6 \).

Step2: Rearrange into standard quadratic form

Move all terms to the left side: \( 5x^2 + 26x + 3x - 6 = 0 \), which simplifies to \( 5x^2 + 29x - 6 = 0 \).

Step3: Factor the quadratic (or use quadratic formula)

Factor: \( 5x^2 + 30x - x - 6 = 0 \), then \( 5x(x + 6) - 1(x + 6) = 0 \), so \( (5x - 1)(x + 6) = 0 \).

Step4: Solve for \( x \)

Set each factor to zero: \( 5x - 1 = 0 \) gives \( x = \frac{1}{5} \), and \( x + 6 = 0 \) gives \( x = -6 \).

Answer:

\( x = -6 \) and \( x = \frac{1}{5} \)