Question

solve the linear system using technology.\\\

$$\begin{cases}-0.2x + 0.9y = 14\\\\-0.6x + 1.5y = 24\\end{cases}$$

\the solution of the system is \\( x = \square \\), \\( y = \square \\).\\(\text{(simplify your answers.)}\\)

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by 3:
$3(-0.2x + 0.9y) = 3(14)$
$-0.6x + 2.7y = 42$

Step2: Subtract second equation

Subtract $-0.6x + 1.5y = 24$ from new equation:
$(-0.6x + 2.7y) - (-0.6x + 1.5y) = 42 - 24$
$1.2y = 18$

Step3: Solve for $y$

Calculate $y$:
$y = \frac{18}{1.2} = 20$

Step4: Substitute $y$ to find $x$

Plug $y=20$ into first equation:
$-0.2x + 0.9(20) = 14$
$-0.2x + 18 = 14$
$-0.2x = 14 - 18 = -4$
$x = \frac{-4}{-0.2} = 25$

Answer:

$x=25$, $y=20$