Question

find the solution of the system of equations.
\\(5x + y = 35\\)
\\(-5x + 5y = -5\\)

Explanation:

Step1: Add the two equations

$$(5x + y) + (-5x + 5y) = 35 + (-5)$$
Simplify:
$$6y = 30$$

Step2: Solve for $y$

$$y = \frac{30}{6} = 5$$

Step3: Substitute $y=5$ into first equation

$$5x + 5 = 35$$

Step4: Solve for $x$

$$5x = 35 - 5 = 30$$
$$x = \frac{30}{5} = 6$$

Answer:

$x=6$, $y=5$