If $2x - 3y = -1$ and $\frac{x}{x+y} = \frac{7}{12}$, then the value of $2xy$ is:
System Equations Setup
We are given two equations:
- $ 2x - 3y = -1 $
- $ \frac{x}{x+y} = \frac{7}{12} $
Our goal is to find the value of $2xy$. First, let's simplify the second equation.
Solving Variables x and y
From the second equation, $\frac{x}{x+y} = \frac{7}{12}$, we cross-multiply:
$ 12x = 7(x+y) $ $ 12x = 7x + 7y $Rearrange to find a relationship between $x$ and $y$:
$ 12x - 7x = 7y $ $ 5x = 7y $We can express $x$ in terms of $y$: $ x = \frac{7}{5}y $
Now, substitute this expression for $x$ into the first equation, $2x - 3y = -1$:
$ 2\left(\frac{7}{5}y\right) - 3y = -1 $ $ \frac{14}{5}y - 3y = -1 $To solve for $y$, find a common denominator:
$ \frac{14}{5}y - \frac{15}{5}y = -1 $ $ \frac{14 - 15}{5}y = -1 $ $ -\frac{1}{5}y = -1 $Multiply both sides by -5:
$ y = 5 $Substitute the value $y=5$ back into the relation $x = \frac{7}{5}y$:
$ x = \frac{7}{5}(5) $ $ x = 7 $So, the values are $x=7$ and $y=5$.
Calculating $2xy$ Value
Finally, calculate the value of $2xy$ using $x=7$ and $y=5$:
$ 2xy = 2(7)(5) $ $ 2xy = 2(35) $ $ 2xy = 70 $Similar Questions
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Important Questions from Linear Equation in 2 Variable
If 2 x + 3 y = 17;
2 x+2 - 3 y+1 = 5
then the values of x and y are:
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