Solve for x and y: 2x- 3y 4 =3, 5x=2y+7 - Vidyadip

Question

Solve for x and y:
$\text{2x}-\frac{\text{3y}}4{}=3,$
$5\text{x}=2\text{y}+7$

✓

Answer

The given equations are: $\text{2x}-\frac{\text{3y}}{4}=3\ \dots(1)$ $\text{5x}=\text{2y}+7\ \dots(2)$ Multiply (1) by 2 and 2 by $\frac{3}{4}$ $\text{4x}-\frac{\text{3y}}{2}=6\ \dots(3)$ $\frac{15}{4}\text{x}-\frac{3}{2}\text{y}-\frac{21}{4}\ \dots(4)$Subtracting (3) from (4), we get
$-\frac{1}{4}\text{x}=-\frac{3}4{}$ $-\text{x}=-3$ $\Rightarrow\text{x}=3$Substitution x = 3 in (1), we get
$2\times3-\frac{\text{3y}}{4}=3$ $-\frac{\text{3y}}{4}=3-6$ $-\frac{\text{3y}}{4}=-3$ $\Rightarrow\text{y}=\frac{-3\times4}{-3}=4$$\therefore$ solution is x = 3 and y = 4

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