Question

solve the linear system using technology.\

$$\begin{cases}0.6x + 0.9y = 12\\\\- 0.2x + 1.5y = 23\\end{cases}$$

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

Explanation:

Step1: Eliminate x variable

Multiply the second equation by 3:
$$3\times(-0.2x + 1.5y) = 3\times23$$
$$-0.6x + 4.5y = 69$$
Add this to the first equation:
$$(0.6x + 0.9y) + (-0.6x + 4.5y) = 12 + 69$$
$$5.4y = 81$$

Step2: Solve for y

Isolate y by dividing:
$$y = \frac{81}{5.4} = 15$$

Step3: Substitute y into first equation

Plug $y=15$ into $0.6x + 0.9y = 12$:
$$0.6x + 0.9\times15 = 12$$
$$0.6x + 13.5 = 12$$

Step4: Solve for x

Isolate x:
$$0.6x = 12 - 13.5$$
$$0.6x = -1.5$$
$$x = \frac{-1.5}{0.6} = -5$$

Answer:

$x=-5$, $y=15$