Solve the system of equations:
$y + 2 z = 7$
$x - y = 3$
$2 x + 3 y + 4 z = 17$

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Solution

$y + 2 z = 7 ⟹ 2 z = 7 - y$
$x - y = 3 ⟹ x = y + 3$
$2 x + 3 y + 4 z = 17 ⟹ 2 (y + 3) + 3 y + 2 (7 - y) = 17 ⟹ 3 y = - 3 ⟹ y = - 1$
$x = y + 3 = 2, z = \frac{7 + 1}{2} = 4$

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