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If 7x + 3y = 45 and 3x + 7y = 35, what is the value of x + y?
8
10
12
6
8
Since the coefficients are symmetric, simply add both equations: (7+3)x + (3+7)y = 45+35, which leads to 10(x+y) = 80.
Two linear equations are provided: 7x + 3y = 45 and 3x + 7y = 35.
(ax+by)+(bx+ay)=(a+b)(x+y)
Since the coefficients are symmetric, simply add both equations: (7+3)x + (3+7)y = 45+35, which leads to 10(x+y) = 80.
Students often try to solve for x and y individually using substitution, which is time-consuming and increases the chance of calculation errors.
Add the two equations
Add the given equations 7x+3y=45 and 3x+7y=35 together.
(7x+3y)+(3x+7y)=45+35
Simplify the sum
Combine the coefficients of x and y to get 10x+10y.
10x+10y=80
Factor out common terms
Factor out 10 from the left side and divide both sides by 10 to find the value of x+y.
10(x+y)=80тЯ╣x+y=1080тАЛ=8
A is correct because summing the equations results in 10(x+y)=80, which simplifies to x+y=8.
This symmetric coefficient trick is highly effective in matrix algebra and systems of linear equations in competitive exams.
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