Question

find all solutions of the system of equations algebraically. write your solutions as coordinate points.

$y = x^2 + 3x - 41$

$16 = 3x - y$

answer
attempt 1 out of 2
two solutions
and

Explanation:

Step1: Isolate y from linear equation

Rearrange $16 = 3x - y$ to solve for $y$:
$y = 3x - 16$

Step2: Substitute y into quadratic equation

Replace $y$ in $y = x^2 + 3x - 41$ with $3x - 16$:
$3x - 16 = x^2 + 3x - 41$

Step3: Simplify to solve for x

Cancel $3x$ on both sides, rearrange terms:
$0 = x^2 - 25$
$x^2 = 25$
$x = \pm 5$

Step4: Find y for x=5

Substitute $x=5$ into $y = 3x - 16$:
$y = 3(5) - 16 = 15 - 16 = -1$

Step5: Find y for x=-5

Substitute $x=-5$ into $y = 3x - 16$:
$y = 3(-5) - 16 = -15 - 16 = -31$

Answer:

$(5, -1)$ and $(-5, -31)$