Answer:
To solve the system of equations:
-2x + y = 0
y = (1/2)x - 3
We can use the method of substitution or elimination. Let's solve it using the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable. In this case, we have y = (1/2)x - 3 from the second equation.
Step 2: Substitute the expression for y in the first equation with the value obtained in step 1. We substitute y with (1/2)x - 3 in -2x + y = 0:
-2x + (1/2)x - 3 = 0
Step 3: Simplify and solve for x:
-4x + x/2 - 3 = 0
-8x + x - 6 = 0
-7x - 6 = 0
-7x = 6
x = -6/7
Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use the second equation:
y = (1/2)(-6/7) - 3
y = -3/7 - 3
y = -3/7 - 21/7
y = -24/7
Therefore, the solution to the system of equations is x = -6/7 and y = -24/7.