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
- Let \(y = \frac{1}{10}x\) and \(x + 50y = 120\). What is the value of x and y?
- The following lines with the equations
$x + 2y = 12$,
$4x + 8y = 48$ - Solutions for the following pair of equations would be
$x + 2y = 6$,
$x - 2y = 16$ 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?
