Question

find the solution of the system of equations.
14x - 4y = 40
7x + 8y = -10
answer attempt 1 out of 2
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Explanation:

Step1: Eliminate $x$ via scaling

Multiply the second equation by 2:
$$2\times(7x + 8y) = 2\times(-10) \implies 14x + 16y = -20$$

Step2: Subtract equations to solve for $y$

Subtract the first equation from the scaled second equation:
$$(14x + 16y) - (14x - 4y) = -20 - 40$$
$$20y = -60 \implies y = \frac{-60}{20} = -3$$

Step3: Substitute $y$ to find $x$

Plug $y=-3$ into $14x - 4y = 40$:
$$14x - 4\times(-3) = 40 \implies 14x + 12 = 40$$
$$14x = 40 - 12 = 28 \implies x = \frac{28}{14} = 2$$

Answer:

$(2, -3)$