Linear Equations: Solve for x and y
Given the system of two linear equations:
- Equation 1: \(y = \frac{1}{10}x\)
- Equation 2: \(x + 50y = 120\)
The objective is to determine the specific numerical values for x and y that satisfy both equations simultaneously.
Applying the Substitution Method
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Substitute the expression for \(y\) from Equation 1 into Equation 2:
\(x + 50 \left( \frac{1}{10}x \right) = 120\)
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Simplify and Solve for x:
Combine terms involving \(x\): \(x + \frac{50}{10}x = 120\) \(x + 5x = 120\) \(6x = 120\)
Isolate \(x\) by dividing both sides by 6: \(x = \frac{120}{6}\) \(x = 20\)
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Solve for y:
Substitute the value \(x = 20\) back into Equation 1: \(y = \frac{1}{10}(20)\) \(y = \frac{20}{10}\) \(y = 2\)
Thus, the solution to the system of equations is x = 20 and y = 2.
Similar Questions
- The following lines with the equations
$x + 2y = 12$,
$4x + 8y = 48$ - Solutions for the following pair of equations would be
$x + 2y = 6$,
$x - 2y = 16$ - 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?
