Solve the simultaneous equations A + B = 32 and A - B = 18.
From NCERTAsked by Mrinal U.24 Oct 2026, 12:29 PM ISTUpdated
The answer
The values that solve both equations are:
A = 25
B = 7
On the board
We are given two equations: A plus B equals 32, and A minus B equals 18. We need to find the values of A and B.
(A + B) + (A - B) = 32 + 18
checked
First, add both equations to eliminate B and solve for A.
2A = 50
checked
Simplify the left side: B cancels out, so we have 2A.
A = 25
checked
Divide both sides by 2 to find the value of A.
25 + B = 32
checked
Now substitute A = 25 into the first equation to find B.
B = 7
checked
Subtract 25 from both sides to get the value of B.
Answer
A = 25;\ B = 7
A equals 25 and B equals 7.
Every ticked line was worked again and checked by the computer (SymPy 1.11.1).
Why each step works
Add both equations:
(A + B) + (A - B) = 32 + 18. When you add, B and -B cancel each other (B - B = 0). This leaves only A terms, making it easy to solve for A.
Simplify:
2A = 50. Both A's add up, so you get 2A. The numbers on the right also add up.
Divide by 2:
A = 25. To find just one A, divide both sides by 2.
Substitute A = 25 into the first equation:
25 + B = 32. Now you know A, so you can find B easily.
Subtract 25 from both sides:
B = 7. This gives you the value of B.
Solving Simultaneous Equations (A + B = 32, A - B = 18)
Add both equations: (A + B) + (A - B) = 32 + 18
Simplify: 2A = 50
Divide by 2: A = 25
Substitute A = 25 into first equation: 25 + B = 32
Solve for B: B = 7
Check your answer
Put A = 25 and B = 7 back into both equations:
First equation: 25 + 7 = 32 ✔️
Second equation: 25 - 7 = 18 ✔️
Both are correct, so your answers are right.
Common mistakes
Forgetting to add the equations: Some students try to solve for A or B directly and get stuck. Adding or subtracting equations helps to remove one variable.
Wrong sign when substituting: If you use the wrong sign (like using -B instead of +B), you will get the wrong answer.
Not checking the answer: Always put your answers back into the original equations to be sure.
Try one yourself
Solve these equations:
X + Y = 40
X - Y = 10
Find the values of X and Y.
Check yourself
If A + B = 32 and A - B = 18, what is the value of A?
A = 25, because adding both equations gives 2A = 50.
Why do we add the equations in this method?
To cancel out B and make it easy to solve for A.
If you got B = -7, what mistake might you have made?
You may have used the wrong sign or made a calculation error when substituting.
Quick recap
Add or subtract equations to remove one variable.
Always check your answers in both equations.
Be careful with signs when substituting values.
Simultaneous equations give values that work for both equations together.
