Sum of two numbers is 35 and their difference is 13.Represent this solution algebracially and graphically. Of maths class 10th ncert of chapter pair of linear equation in two varaibles?

Question

Answer

Let the two numbers be x and y.
As per question sum of two numbers is x+y=35......eq(1)
And their difference is x−y=13...................................eq(2)
On Adding equation 1 and 2 we get
x+y=35
x−y=13
____________
2x=48

Therefore x=24
As per equation (1) x+y=35
Putting the value of x we get,24+y=35
Therefore y=11

Answer

Answer

Answer

Let take X and Y
sum of two numbers is 35 that is X+Y=35
difference of two numbers is 13 that is X-Y=13
simplified the both equations we get 2x=48
then X= 24 and simplify X-Y=13 and put the value of X in this equation then we get y= 11

Answer

Solution to the Pair of Linear Equations

Algebraic Representation:
- Let the two numbers be x and y.
- According to the given conditions:
- x + y = 35
- x - y = 13

Graphical Representation:
- To represent these equations graphically, we first need to convert them into slope-intercept form (y = mx + c).
- From the equations x + y = 35 and x - y = 13, we get:
- y = -x + 35
- y = x - 13
- Plot these two lines on the graph, where the intersection point will be the solution to the system of equations.

Explanation:
- The algebraic representation helps in solving the equations by substitution or elimination method to find the values of x and y.
- The graphical representation visually shows the intersection point where both equations are satisfied simultaneously.
- This concept is a part of the Pair of Linear Equations in Two Variables chapter in Class 10 NCERT Mathematics.
- Understanding and practicing such problems can enhance problem-solving skills and strengthen the understanding of linear equations.

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