Solve by Substitution x+2y=3 , 2x-y=1

Problem

{[x+2*y=3],[2*x−y=1])

Solution

1. Isolate a variable in the first equation by subtracting 2*y from both sides.

x=3−2*y

2. Substitute the expression for x into the second equation.

2*(3−2*y)−y=1

3. Distribute the constant into the parentheses.

6−4*y−y=1

4. Combine like terms to simplify the equation.

6−5*y=1

5. Solve for y by subtracting 6 from both sides and then dividing by −5

−5*y=−5

y=1

6. Substitute the value of y back into the expression for x

x=3−2*(1)

x=1

Final Answer

(x,y)=(1,1)

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