Solving the System of Linear Equations
We are given two linear equations:
- Equation 1: \(2x - y = 7\)
- Equation 2: \(x - y = 6\)
Our goal is to find the values of \(x\) and \(y\) that satisfy both equations.
Elimination Method
We can use the elimination method by subtracting Equation 2 from Equation 1. This will help eliminate the variable \(y\).
- Subtract Equation 2 from Equation 1: \((2x - y) - (x - y) = 7 - 6\)
- Simplify the equation: \(2x - y - x + y = 1\) \(x = 1\)
- Substitute the value of \(x\) (which is 1) back into Equation 2 (\(x - y = 6\)): \(1 - y = 6\)
- Solve for \(y\): \(-y = 6 - 1\) \(-y = 5\) \(y = -5\)
Thus, the values are \(x=1\) and \(y=-5\). This matches the pair \((1, -5)\).
Similar Questions
- The following lines with the equations
$x + 2y = 12$,
$4x + 8y = 48$ - Solutions for the following pair of equations would be
$x + 2y = 6$,
$x - 2y = 16$
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)
