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
What is the solution of the following equations ?
2x + 3y = 12 and 3x − 2y = 5
Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:
When 5 children from class A join class B, the number of children in both classes is the same. If 25 children from B, join A, then the number of children in A becomes double the number of children in B. The ratio of the number of children in A to those in B is:
If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x 3+ 216y 3)?
If 8k 6+ 15k 3– 2 = 0, then the positive value of \(\left( {{\rm{k}}\,{\rm{ + }}\,\frac{1}{{\rm{k}}}} \right)\) is :
