$x + 2y = 6$,
$x - 2y = 16$
Solving Linear Equation System
We need to solve the following system of linear equations:
- Equation 1: $x + 2y = 6$
- Equation 2: $x - 2y = 16$
Step-by-Step Solution using Elimination
- Add the two equations to eliminate the variable $y$. The terms $+2y$ and $-2y$ will cancel out.
$ (x + 2y) + (x - 2y) = 6 + 16 $
$ 2x = 22 $
- Solve for $x$ by dividing both sides by 2.
$ x = \frac{22}{2} $
$ x = 11 $
- Substitute the value of $x$ (which is 11) back into either Equation 1 or Equation 2 to find $y$. Let's use Equation 1.
$ 11 + 2y = 6 $
- Solve for $y$. Subtract 11 from both sides.
$ 2y = 6 - 11 $
$ 2y = -5 $
Divide both sides by 2.$ y = \frac{-5}{2} $
Final Solution
The solution to the system of equations is $x = 11$ and $y = -\frac{5}{2}$.
Similar Questions
- Let \(y = \frac{1}{10}x\) and \(x + 50y = 120\). What is the value of x and y?
- The following lines with the equations
$x + 2y = 12$,
$4x + 8y = 48$ - If \(2x-y=7\) and \(x-y=6\), then value of x and y will be
The taxi charges in a city consist of a fixed charge together with the charge per kilometre for the distance covered. For a distance of 35 km, the charge paid is ₹375 and for a distance of 48 km, the charge paid is ₹427. Find the fixed charges and the charge per km (in ₹), respectively.
Important Questions from Linear Equation in 2 Variable
The cost of 6 pens and 19 pencils is ₹275. If the cost of a pen decreases by ₹7 and the cost of a pencil increases by ₹7, then the cost of 15 pens and 4 pencils is 132. What is the original cost of 6 pens and 2 pencils?
- The cost of 12 pens and 7 pencils is ₹285. If the cost of a pen decreases by ₹6 and the cost of a pencil increases by ₹5, then the cost of 11 pens and 3 pencils is ₹118. What is the original cost of 2 pens and 2 pencils?
- The cost of 7 pens and 17 pencils is ₹92. If the cost of a pen decreases by ₹0.50 and the cost of a pencil increases by ₹8, then the cost of 8 pens and 14 pencils is 186. What is the original cost of 9 pens and 6 pencils?
- The cost of 19 pens and 13 pencils is ₹254. If the cost of a pen decreases by ₹6 and the cost of a pencil increases by ₹9, then the cost of 14 pens and 2 pencils is ₹106. What is the original cost of 12 pens and 15 pencils?
- The price of 4 pens and 5 notebooks is ₹130. If the price of a pen increases by 25% and the price of a notebook decreases by 20%, then the price of 2 pens and 4 notebooks becomes ₹82. What is the original price of 1 pen and 2 notebooks?
