Question

solve the following system using any method.
$6x - 8y = -13$
$3x + 2y = 7.3$

Explanation:

Step1: Eliminate $x$ via scaling

Multiply the second equation by 2:
$$2\times(3x + 2y) = 2\times7.3$$
$$6x + 4y = 14.6$$

Step2: Subtract equations to solve for $y$

Subtract the first original equation from the scaled equation:
$$(6x + 4y) - (6x - 8y) = 14.6 - (-13)$$
$$12y = 27.6$$
$$y = \frac{27.6}{12} = 2.3$$

Step3: Substitute $y$ to find $x$

Plug $y=2.3$ into $3x + 2y = 7.3$:
$$3x + 2\times2.3 = 7.3$$
$$3x + 4.6 = 7.3$$
$$3x = 7.3 - 4.6 = 2.7$$
$$x = \frac{2.7}{3} = 0.9$$

Answer:

$x=0.9$, $y=2.3$