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 = \boxed{25}, y = \boxed{20}.\\(\text{simplify your answers.}\\)

Explanation:

Step1: Eliminate x variable

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

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

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

Step4: Substitute y into first equation

Plug $y=20$ into $-0.2x + 0.9y = 14$:
$$-0.2x + 0.9(20) = 14 \implies -0.2x + 18 = 14$$

Step5: Solve for x

Isolate x:
$$-0.2x = 14 - 18 = -4$$
$$x = \frac{-4}{-0.2} = 25$$

Answer:

$x=25$, $y=20$