The solution of the system of equation \(5x+2y = 29\) ; \(x+4y =13\) will be (3,2) and this can be determined by using the arithmetic operations.
Given :
\(5x+2y = 29\) ----- (1)
\(x+4y =13\) ----- (2)
Now, solve for x in equation (2).
\(x = 13-4y\) --- (3)
Now, put the value of x obtained above in equation (1).
\(5(13-4y)+2y=29\)
\(65-20y+2y=29\)
\(36=18y\)
\(y=2\)
Now, put the value of y in equation (3).
\(x=13-(4\times 2)\)
\(x=5\)
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