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If 3x + 2y = 12 and 2x + 3y = 13, find the value of x + y.
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Since the coefficients of x and y are symmetric (3,2 and 2,3), add both equations directly to quickly find the sum of x and y without finding their individual values.
Linear equations in two variables: 3x+2y=12 and 2x+3y=13.
(3x+2y)+(2x+3y)=12+13
Since the coefficients of x and y are symmetric (3,2 and 2,3), add both equations directly to quickly find the sum of x and y without finding their individual values.
Students waste valuable exam time by solving the equations simultaneously using elimination or substitution to find x and y individually instead of adding the equations directly.
Write down the given equations
We are given two linear equations: Equation (1) is 3x+2y=12 and Equation (2) is 2x+3y=13.
{3x+2y=122x+3y=13тАЛ
Add both equations together
Add the left-hand sides and right-hand sides of both equations to combine the coefficients of x and y.
(3x+2y)+(2x+3y)=12+13
Simplify the combined equation
Combine like terms: 3x+2x=5x and 2y+3y=5y, which gives 5(x+y)=25.
5x+5y=25тЯ╣5(x+y)=25
Solve for x+y
Divide both sides by 5 to find the final value of x+y.
x+y=525тАЛ=5
A is correct because adding the two equations yields 5(x+y)=25, which simplifies to x+y=5.
Symmetric equations with swapped coefficients frequently appear in competitive exams; always check if adding or subtracting the equations as a whole simplifies the problem.
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