Solving for the Largest Number
We are given the sum and difference of two numbers and need to find the larger one.
Problem Setup
Let the two numbers be $x$ and $y$, where $x$ represents the largest number.
We can set up two equations based on the given information:
- Sum: $x + y = 33$
- Difference: $x - y = 13$
Calculating the Largest Number
To find the value of $x$, we can add the two equations together. This method eliminates $y$.
Equation 1: $x + y = 33$
Equation 2: $x - y = 13$
Add Equation 1 and Equation 2:
$ (x + y) + (x - y) = 33 + 13 $
Simplifying the equation:
$ 2x = 46 $
Solve for $x$ by dividing both sides by 2:
$ x = \frac{46}{2} $
$ x = 23 $
Result
The largest number is 23.
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Important Questions from Linear Equation in 2 Variable
What is the solution of the following equations ?
2x + 3y = 12 and 3x − 2y = 5
Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:
When 5 children from class A join class B, the number of children in both classes is the same. If 25 children from B, join A, then the number of children in A becomes double the number of children in B. The ratio of the number of children in A to those in B is:
If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x 3+ 216y 3)?
If 8k 6+ 15k 3– 2 = 0, then the positive value of \(\left( {{\rm{k}}\,{\rm{ + }}\,\frac{1}{{\rm{k}}}} \right)\) is :
