Question

1. \

$$\begin{cases}x - 3y = -24 \\\\ 5x + 8y = -5\\end{cases}$$

1. \

$$\begin{cases}5x + 3y = 15 \\\\ x - 6y = 3\\end{cases}$$

Explanation:

(Problem 7):

Step1: Isolate $x$ from first equation

$x = 3y - 24$

Step2: Substitute $x$ into second equation

$5(3y - 24) + 8y = -5$

Step3: Simplify and solve for $y$

$15y - 120 + 8y = -5$
$23y = 115$
$y = 5$

Step4: Substitute $y=5$ back to find $x$

$x = 3(5) - 24 = 15 - 24 = -9$

(Problem 8):

Step1: Isolate $x$ from second equation

$x = 6y + 3$

Step2: Substitute $x$ into first equation

$5(6y + 3) + 3y = 15$

Step3: Simplify and solve for $y$

$30y + 15 + 3y = 15$
$33y = 0$
$y = 0$

Step4: Substitute $y=0$ back to find $x$

$x = 6(0) + 3 = 3$

Answer:

Problem 7: $x=-9$, $y=5$
Problem 8: $x=3$, $y=0$