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
-
Substitute the expression for \(y\) from Equation 1 into Equation 2:
\(x + 50 \left( \frac{1}{10}x \right) = 120\)
-
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: \(x = \frac{120}{6}\) \(x = 20\)
-
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
$x + 2y = 6$,
$x - 2y = 16$
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)
