Question
Solve for x and y:
$\text{4x}-\text{3y}=8,$
$\text{6x}-\text{y}=\frac{29}{3}$
$\text{4x}-\text{3y}=8,$
$\text{6x}-\text{y}=\frac{29}{3}$
✓
Answer
The given equations are: $\text{4x}-\text{3y}=8\ \dots(1)$ $\text{6x}-\text{y}=\frac{29}{3}\ \dots(2)$ Multiply (1) by 2 and 2 by 3 $\text{4x}-\text{3y}=8\ \dots(3)$ $\text{18x}-\text{3y}=29\ \dots(4)$Subtracting (3) from (4), we get
$\text{14x}=21$ $\Rightarrow\text{x}=\frac{21}{14}=\frac{3}{2}$Substitution $\text{x}=\frac{3}{2}$ in (1), we get
$2\times\frac{3}{2}-\text{3y}=8$ $\Rightarrow6-\text{3y}=8$ $-\text{3y}=2$ $\Rightarrow\text{y}=\frac{-2}{3}$$\therefore$ Solution is $\text{x}=\frac{3}{2}$ and $\text{y}=\frac{-2}{3}$
$\text{14x}=21$ $\Rightarrow\text{x}=\frac{21}{14}=\frac{3}{2}$Substitution $\text{x}=\frac{3}{2}$ in (1), we get
$2\times\frac{3}{2}-\text{3y}=8$ $\Rightarrow6-\text{3y}=8$ $-\text{3y}=2$ $\Rightarrow\text{y}=\frac{-2}{3}$$\therefore$ Solution is $\text{x}=\frac{3}{2}$ and $\text{y}=\frac{-2}{3}$
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