Question

solve the linear system using technology
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$$\begin{cases} 0.2x + 0.3y = 2 \\\\ -0.6x + 1.3y = 5 \\end{cases}$$

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

Explanation:

Step1: Eliminate x variable

Multiply first equation by 3:
$3*(0.2x + 0.3y) = 3*2$
$\Rightarrow 0.6x + 0.9y = 6$

Step2: Add to second equation

Add new equation to $-0.6x + 1.3y = 5$:
$(0.6x - 0.6x) + (0.9y + 1.3y) = 6 + 5$
$\Rightarrow 2.2y = 11$

Step3: Solve for y

Isolate y:
$y = \frac{11}{2.2} = 6$

Step4: Substitute y to find x

Plug $y=6$ into $0.2x + 0.3y = 2$:
$0.2x + 0.3*6 = 2$
$\Rightarrow 0.2x + 1.8 = 2$
$\Rightarrow 0.2x = 0.2$
$\Rightarrow x = 1$

Answer:

$x=1$, $y=6$