Question

solve the following system of equations.\
\\(\

$$\begin{cases} y = x^2 - 8x \\\\ -2x + y = -21 \\end{cases}$$

\\)\
if there is more than one solution, use the \\or\\\ button.\
\\((x, y) = (\square, \square)\\)

Explanation:

Step1: Substitute $y$ into linear equation

Substitute $y=x^2-8x$ into $-2x+y=-21$:
$$-2x + (x^2 - 8x) = -21$$

Step2: Simplify to quadratic equation

Combine like terms and rearrange:
$$x^2 - 10x + 21 = 0$$

Step3: Factor the quadratic equation

Find two factors of 21 that sum to -10:
$$(x-3)(x-7) = 0$$

Step4: Solve for $x$ values

Set each factor equal to 0:
$x-3=0 \implies x=3$; $x-7=0 \implies x=7$

Step5: Find corresponding $y$ values

For $x=3$: $y=3^2 -8(3)=9-24=-15$
For $x=7$: $y=7^2 -8(7)=49-56=-7$

Answer:

$(x,y)=(3, -15)$ or $(7, -7)$