Question

solve the following system of equations.\\(-1.2x + 0.2y = 8\\)\\(0.8x + 1.2y = -8\\)\\(x = \square\\)\\(y = \square\\)

Explanation:

Step1: Eliminate decimals

Multiply both equations by 10:
$-12x + 2y = 80$
$8x + 12y = -80$

Step2: Simplify first equation

Divide first equation by 2:
$-6x + y = 40$
Rearrange to isolate $y$:
$y = 6x + 40$

Step3: Substitute $y$ into second equation

Substitute $y=6x+40$ into $8x + 12y = -80$:
$8x + 12(6x + 40) = -80$
Expand and simplify:
$8x + 72x + 480 = -80$
$80x + 480 = -80$

Step4: Solve for $x$

Subtract 480 from both sides:
$80x = -80 - 480$
$80x = -560$
Divide by 80:
$x = \frac{-560}{80} = -7$

Step5: Solve for $y$

Substitute $x=-7$ into $y=6x+40$:
$y = 6(-7) + 40$
$y = -42 + 40 = -2$

Answer:

$x = -7$
$y = -2$