Question

solve the following system of equations algebraically:

$y = x^2 + 7x - 10$

$y = x - 10$

answer
attempt 2 out of 2
two solutions
and

Explanation:

Step1: Set equations equal

Since both equal $y$, equate them:
$x^2 + 7x - 10 = x - 10$

Step2: Simplify the equation

Subtract $x-10$ from both sides:
$x^2 + 7x - 10 - x + 10 = 0$
$x^2 + 6x = 0$

Step3: Factor the quadratic

Factor out $x$:
$x(x + 6) = 0$

Step4: Solve for $x$

Set each factor to 0:
$x = 0$ or $x + 6 = 0 \implies x = -6$

Step5: Find corresponding $y$

For $x=0$: $y = 0 - 10 = -10$
For $x=-6$: $y = -6 - 10 = -16$

Answer:

$(0, -10)$ and $(-6, -16)$