Question

solve the linear system using technology.\

$$\begin{cases}0.2x + 0.9y = 5\\\\0.6x + 1.5y = 9\\end{cases}$$

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

Explanation:

Step1: Eliminate x variable

Multiply first equation by 3:
$$3*(0.2x + 0.9y) = 3*5$$
$$0.6x + 2.7y = 15$$

Step2: Subtract second equation

Subtract $0.6x + 1.5y = 9$ from new equation:
$$(0.6x + 2.7y) - (0.6x + 1.5y) = 15 - 9$$
$$1.2y = 6$$

Step3: Solve for y

Isolate y:
$$y = \frac{6}{1.2} = 5$$

Step4: Substitute y into first equation

Plug $y=5$ into $0.2x + 0.9y = 5$:
$$0.2x + 0.9*5 = 5$$
$$0.2x + 4.5 = 5$$

Step5: Solve for x

Isolate x:
$$0.2x = 5 - 4.5 = 0.5$$
$$x = \frac{0.5}{0.2} = 5$$

Answer:

$x=5$, $y=5$