Final answer:
To solve the system of equations {2x - y = 0, x - 2y = 0}, you can use the method of substitution. The solution to the system of equations is x = 0 and y = 0.
Step-by-step explanation:
To solve the system of equations {2x - y = 0, x - 2y = 0}, we can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
From the first equation, we can solve for y in terms of x: y = 2x.
Step 2: Substitute the expression for the variable found in step 1 into the other equation.
Substituting y = 2x into the second equation, we get x - 2(2x) = 0. Simplifying this equation gives us -3x = 0.
Step 3: Solve for the remaining variable.
Since -3x = 0, we can divide both sides by -3 to get x = 0.
Step 4: Substitute the value found in step 3 back into one of the original equations to solve for the other variable.
Using the first equation, we substitute x = 0 to find y: 2(0) - y = 0. Solving for y gives us y = 0.
Therefore, the solution to the system of equations is x = 0 and y = 0.