Question

solve the following system using the elimination method.
$7x - 2y = 8$
$4x + 5y = -9.25$

Explanation:

Step1: Eliminate $y$ via scaling

Multiply first eq by 5: $5(7x - 2y) = 5(8) \implies 35x - 10y = 40$
Multiply second eq by 2: $2(4x + 5y) = 2(-9.25) \implies 8x + 10y = -18.5$

Step2: Add scaled equations

Add the two new equations:
$$(35x - 10y) + (8x + 10y) = 40 + (-18.5)$$
$$43x = 21.5$$

Step3: Solve for $x$

Isolate $x$:
$$x = \frac{21.5}{43} = 0.5$$

Step4: Substitute $x$ to find $y$

Plug $x=0.5$ into $7x - 2y = 8$:
$$7(0.5) - 2y = 8$$
$$3.5 - 2y = 8$$
$$-2y = 8 - 3.5$$
$$-2y = 4.5$$
$$y = \frac{4.5}{-2} = -2.25$$

Answer:

$x=0.5$, $y=-2.25$