$x + 2y = 6$,
$x - 2y = 16$
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
- The following lines with the equations
$x + 2y = 12$,
$4x + 8y = 48$
Important Questions from Linear Equation in 2 Variable
The sum of two numbers m and n is 84 (m > n) and their difference is 6. What is the ratio of the two numbers?
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?
A. 10 m
B. 14 m
C. 12 m
D. 8 m
What historic achievement did Manu Bhaker accomplish at the 2024 Paris Olympics?
The sum of a two digit number and the number formed by interchanging its digit is 132. If nine is subtracted from the first number, the new number is 3 more than 6 times of the sum of the digits in the first number. Find the first number.
Which of the following options is the solution of the given equation:-
2x - 4y = 16
A. (8, -1)
B. (5, -5)
C. (6, -1)
D. (9, 2)
