Question

solve the linear system using technology.\\\

$$\begin{cases} 0.2x + 0.3y = 2 \\\\ -0.6x + 1.3y = 5 \\end{cases}$$

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

Explanation:

Step1: Eliminate decimals

Multiply both equations by 10:
$2x + 3y = 20$
$-6x + 13y = 50$

Step2: Scale first equation

Multiply first equation by 3:
$6x + 9y = 60$

Step3: Add equations to eliminate $x$

Add scaled first equation to second equation:
$$(6x + 9y) + (-6x + 13y) = 60 + 50$$
$$22y = 110$$

Step4: Solve for $y$

Divide both sides by 22:
$y = \frac{110}{22} = 6$

Step5: Substitute $y$ to find $x$

Plug $y=6$ into $2x + 3y = 20$:
$2x + 3(6) = 20$
$2x + 18 = 20$
$2x = 2$
$x = 1$

Answer:

$x = 1$, $y = 6$