Solve for x and y 7(y + 3) - 2(x + 2) = 14, 4(y - 2) + 3(x - 3) =… - Vidyadip

Question

Solve for $x$ and $y$
$7(y + 3) - 2(x + 2) = 14,$
$4(y - 2) + 3(x - 3) = 2$

✓

Answer

The given equations are:
$7(y + 3) - 2(x + 2) = 14$
$4(y - 2) + 3(x - 3) = 2$
$7(y + 3) - 2(x + 2) = 14$
$⇒ 7y + 21 - 2x - 4 = 14$
$⇒ 7y - 2x = 14 + 4 - 21$
$⇒ -2x + 7y = -3 ...(1)$
$4(y - 2) + 3(x - 3) = 2$
$⇒ 4y - 8 + 3x - 9 = 2$
$⇒ 4y + 3x = 2 + 8 + 9$
$⇒ 3x + 4y = 19 ...(2)$
Multiply $(1)$ by $4$ and $(2)$ by $7$, we get
$-8x + 28y = -12 ...(3)$
$21x + 28y = 133 ...(4)$
Subtracting $(3)$ and $(4),$ we get
$29x = 145$
$x = 5$
Substituting $x = 5$ in $(1)$, we get
$-2 × 5 + 7y = -3$
$⇒ 7y = -3 + 10$
$⇒ 7y = 7$
$⇒ y = 1$
$\therefore$ Solution is $x = 5$ and $y = 1$

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