# Consider the following system of llinear equations.1/3x+y=5/42/3x-4/3y=5/3Part A: (What property)/(properties) can be used to write an equivalent system?Part B: Write an equivalent system and use elimination method to solve for x and y.

Consider the following system of llinear equations.
$\frac{1}{3}x+y=\frac{5}{4}$
$\frac{2}{3}x-\frac{4}{3}y=\frac{5}{3}$
Part A: can be used to write an equivalent system?
Part B: Write an equivalent system and use elimination method to solve for x and y.

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Arnold Odonnell
Step 1: Given,
The linear equations
$\frac{1}{3}x+y=\frac{5}{4}$
$\frac{2}{3}x-\frac{4}{3}y=\frac{5}{3}$
we have to solve these equations by eliminating methods.
Step 2
A.
When multiplying, changing the order of the numbers does not change the product.
B.
Mult. equation (1) by $\frac{4}{3}$ and add both equations, we get
$\frac{4}{9}x+\frac{4}{3}y=\frac{5}{3}$
$\frac{2}{3}x-\frac{4}{3}y=\frac{5}{3}$
we get x=0, put this value in one of the above equation we get
$\frac{1}{3}×0+y=\frac{5}{4}$
$y=\frac{5}{4}$
Hence the solution of the given system is (0, $\frac{5}{4}$).
Jeffrey Jordon