Question

solve the following system of equations.\
\\( x + 8y = 23 \\)\
\\( -x - 10y = -27 \\)\
\\( x = \square \\)\
\\( y = \square \\)

Explanation:

Step1: Add the two equations

$$(x + 8y) + (-x - 10y) = 23 + (-27)$$
Simplify: $-2y = -4$

Step2: Solve for $y$

$$y = \frac{-4}{-2} = 2$$

Step3: Substitute $y=2$ into first equation

$$x + 8(2) = 23$$
Simplify: $x + 16 = 23$

Step4: Solve for $x$

$$x = 23 - 16 = 7$$

Answer:

$x=7$
$y=2$