Question

x + y = 10\
2x + 3y = 24

Explanation:

Step1: Define the system of equations

We have the linear system:

$$\begin{cases} x + y = 6 \\ 2x + 3y = 14 \end{cases}$$

Step2: Isolate $x$ from first equation

Rearrange $x + y = 6$ to solve for $x$:
$x = 6 - y$

Step3: Substitute $x$ into second equation

Replace $x$ in $2x + 3y = 14$:
$2(6 - y) + 3y = 14$
Expand and simplify:
$12 - 2y + 3y = 14$
$12 + y = 14$

Step4: Solve for $y$

Subtract 12 from both sides:
$y = 14 - 12 = 2$

Step5: Solve for $x$ using $y=2$

Substitute $y=2$ into $x = 6 - y$:
$x = 6 - 2 = 4$

Answer:

$x=4$, $y=2$