Question

find all solutions of the system of equations algebraically. write your solutions as coordinate points.
$y = 2x^2 - 23x + 50$
$3x + y = 18$
answer attempt 1 out of 2
two solutions
and
submit answer

Explanation:

Step1: Isolate y from linear equation

$y = 18 - 3x$

Step2: Substitute y into quadratic equation

$18 - 3x = 2x^2 - 23x + 50$

Step3: Rearrange to standard quadratic form

$2x^2 - 20x + 32 = 0$
Divide by 2: $x^2 - 10x + 16 = 0$

Step4: Factor the quadratic

$(x - 2)(x - 8) = 0$
Solve for x: $x=2$ or $x=8$

Step5: Find y for each x

For $x=2$: $y=18-3(2)=12$
For $x=8$: $y=18-3(8)=-6$

Answer:

$(2, 12)$ and $(8, -6)$