Question
Solve for x and y:
$\frac{\text{x}}{3}+\frac{\text{y}}{4}=11$
$\frac{\text{5x}}{6}-\frac{\text{y}}{3}=-7$
$\frac{\text{x}}{3}+\frac{\text{y}}{4}=11$
$\frac{\text{5x}}{6}-\frac{\text{y}}{3}=-7$
✓
Answer
The given equations are: $\frac{\text{x}}{3}+\frac{\text{y}}{4}=11$ $\frac{\text{5x}}{6}-\frac{\text{y}}{3}=-7$ $\frac{\text{x}}{3}+\frac{\text{y}}{4}=11$ (by taking LCM) $\frac{\text{4x}+3\text{y}}{12}=11$ $\text{4x}+\text{3y}=132\ \dots(1)$ $\frac{\text{5x}}{6}-\frac{\text{y}}{3}=-7$ (by taking LCM) $\frac{\text{5x}-\text{2y}}{6}=-7$ $\text{5x}-\text{2y}=-42\ \dots(2)$ $\text{4x}+\text{3y}=132$ $\text{5x}-\text{2y}=-42$ Multiply (1) by 2 and (2) by 3 8x + 6y = 264 ...(3) 15x - 6y = -126 ...(4)Adding (3) from (4), we get
23x = 138
⇒ x = 6
Substitution x = 6 in (1), we get
4 × 6 + 3y = 132
⇒ 3y = 132 - 24
⇒ 3y = 108
⇒ y = 36
$\therefore$ Solution is x = 6 and y = 36
23x = 138
⇒ x = 6
Substitution x = 6 in (1), we get
4 × 6 + 3y = 132
⇒ 3y = 132 - 24
⇒ 3y = 108
⇒ y = 36
$\therefore$ Solution is x = 6 and y = 36
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