Final answer:
The solution to the system of equations y=2x-3 and y=-1/2x-3 is found using substitution, resulting in x=0 and y=-3. The final answer is the point (0, -3).
Step-by-step explanation:
To solve the system of equations y=2x-3 and y=-1/2x-3, we can use the substitution method since both equations are already solved for y. We set the two equations equal to each other because they both equal y:
2x - 3 = -1/2x - 3
Add 1/2x to both sides to get all x terms on one side:
2x + 1/2x - 3 = -3
Combine like terms:
(5/2)x - 3 = -3
Add 3 to both sides to isolate the x term:
(5/2)x = 0
Now divide by (5/2) to solve for x:
x = 0 / (5/2)
x = 0
Substitute x=0 into one of the original equations to solve for y:
y = 2(0) - 3
y = -3
The solution to the system of equations is (0, -3).