Question

natalias mistake
natalia made a mistake as she solved the system of equations
from the previous screen:
$5x - 2y = 15$
$y = 3x - 12$
what did natalia do well? what should she fix?
natalia
$5x - 2y = 15$
$y = 3x - 12$
$5x - 2(3x - 12) = 15$
$5x - 6x - 24 = 15$
$-x = 39$
$x = -39$

Explanation:

Step1: Identify substitution error

Natalia substituted $y=3x-12$ into $5x-2y=15$, but incorrectly expanded $-2(3x-12)$ as $-6x-24$ instead of $-6x+24$.

Step2: Correct the expansion

$$5x - 2(3x - 12) = 5x - 6x + 24 = 15$$

Step3: Simplify to solve for $x$

$$-x + 24 = 15$$
$$-x = 15 - 24$$
$$-x = -9$$
$$x = 9$$

Step4: Solve for $y$

Substitute $x=9$ into $y=3x-12$:
$$y = 3(9) - 12 = 27 - 12 = 15$$

Answer:

What Natalia did well: She correctly identified the substitution method and chose to substitute $y=3x-12$ into the first equation, which is the right approach for solving this system.
What she should fix: She made a sign error when expanding $-2(3x-12)$; she calculated it as $-6x-24$ instead of $-6x+24$. Correcting this gives the proper solution: $x=9$, $y=15$.