Question

solve the following system of equations.
0.5x + 0.8y = 2
1.5x - 0.6y = -9
x =

y =

Explanation:

Step1: Eliminate decimals, scale equations

Multiply first equation by 10: $5x + 8y = 20$
Multiply second equation by 10: $15x - 6y = -90$

Step2: Scale to eliminate $x$

Multiply first new equation by 3: $15x + 24y = 60$

Step3: Subtract equations to solve for $y$

Subtract $15x - 6y = -90$ from $15x + 24y = 60$:
$$(15x + 24y) - (15x - 6y) = 60 - (-90)$$
$$30y = 150$$
$$y = 5$$

Step4: Substitute $y=5$ to find $x$

Plug $y=5$ into $5x + 8y = 20$:
$$5x + 8(5) = 20$$
$$5x + 40 = 20$$
$$5x = -20$$
$$x = -4$$

Answer:

$x = -4$
$y = 5$